\(149\mathbf{\color{blue}{\;=\;}}74+75\) (som van opeenvolgende gehele getallen)

\(149\mathbf{\color{blue}{\;=\;}}6^2+7^2+8^2\mathbf{\color{blue}{\;=\;}}36+49+64\) (som van opeenvolgende kwadraten)

\(149\mathbf{\color{blue}{\;=\;}}((0;0;7;10)\,(0;1;2;12)\,(0;2;8;9)\,(0;6;7;8)\,(2;3;6;10)\,(4;4;6;9))\lower2pt{\Large{\color{teal}{➋}}}\to\{\#6\}\)

\(149\mathbf{\color{blue}{\;=\;}}2^3+2^3+2^3+5^3\mathbf{\color{blue}{\;=\;}}((0;0;0;0;0;2;2;2;5)\,(0;1;1;1;1;3;3;3;4)\,(1;1;1;1;1;2;2;4;4))\lower2pt{\Large{\color{teal}{➌}}}\to\{\#3\}\)

\(149\mathbf{\color{blue}{\;=\;}}9^2+10^2-2^5\)

\(149\mathbf{\color{blue}{\;=\;}}2^2+2^6+3^4\)

\(149\mathbf{\color{blue}{\;=\;}}23+43+83\) (som van \(3\) priemgetallen die niet de som van twee kwadraten zijn)

\(149\mathbf{\color{blue}{\;=\;}}14*9+14+9\)

\(149\mathbf{\color{blue}{\;=\;}}7^2+10^2\mathbf{\color{blue}{\;=\;}}13^3-2^{11}\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{75^2-74^2}\)

149.1

\(149\mathbf{\color{blue}{\;=\;}}\)(som van drie derdemachten)

\(\qquad~~~~\)References Sum of Three Cubes

\(\qquad~~~~\)Getallen van de vorm \(~9m+4~\) of \(~9m+5~\) kunnen nooit als som van drie derdemachten geschreven worden.

\(\qquad~~~~\)In dit geval is \(m=16~~(+5)\).

\(149\mathbf{\color{blue}{\;=\;}}\)(som van vier derdemachten)

\(\qquad~~~~(z\gt1000)\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{2^3+2^3+2^3+5^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{5^3+8^3+8^3+(-10)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{2^3+(-10)^3+(-19)^3+20^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{11^3+(-19)^3+(-43)^3+44^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-7)^3+(-19)^3+(-49)^3+50^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-13)^3+(-31)^3+(-103)^3+104^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{29^3+98^3+98^3+(-124)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{2^3+104^3+116^3+(-139)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-13)^3+(-73)^3+(-133)^3+140^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{50^3+(-82)^3+(-139)^3+146^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{86^3+(-139)^3+(-142)^3+170^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-55)^3+(-64)^3+(-187)^3+191^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-52)^3+(-115)^3+(-178)^3+194^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{44^3+80^3+197^3+(-202)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{59^3+(-157)^3+(-244)^3+263^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-97)^3+110^3+263^3+(-265)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-160)^3+212^3+269^3+(-292)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-115)^3+152^3+284^3+(-292)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{107^3+134^3+287^3+(-301)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-118)^3+(-187)^3+(-298)^3+326^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{110^3+(-139)^3+(-334)^3+338^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-202)^3+254^3+332^3+(-355)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-139)^3+281^3+302^3+(-361)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{140^3+(-262)^3+(-322)^3+365^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-1)^3+260^3+317^3+(-367)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-103)^3+206^3+347^3+(-367)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-127)^3+(-145)^3+(-355)^3+368^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{44^3+197^3+422^3+(-436)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{332^3+(-349)^3+(-439)^3+449^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{173^3+326^3+386^3+(-460)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-199)^3+293^3+431^3+(-460)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-187)^3+(-283)^3+(-421)^3+470^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-61)^3+(-190)^3+(-481)^3+491^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-145)^3+(-244)^3+(-505)^3+527^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{35^3+(-97)^3+(-538)^3+539^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{134^3+344^3+494^3+(-547)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-235)^3+(-454)^3+(-472)^3+596^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-310)^3+485^3+506^3+(-598)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-52)^3+389^3+563^3+(-619)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{215^3+(-223)^3+(-619)^3+620^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{35^3+(-493)^3+(-496)^3+623^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{275^3+(-307)^3+(-619)^3+626^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-115)^3+(-148)^3+(-628)^3+632^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-250)^3+263^3+653^3+(-655)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-139)^3+(-460)^3+(-571)^3+659^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{395^3+(-538)^3+(-577)^3+659^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{296^3+365^3+638^3+(-694)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{296^3+(-469)^3+(-637)^3+695^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{32^3+143^3+701^3+(-703)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{29^3+146^3+722^3+(-724)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{254^3+(-454)^3+(-700)^3+749^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{215^3+326^3+743^3+(-769)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-139)^3+(-343)^3+(-745)^3+770^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{176^3+521^3+683^3+(-775)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-205)^3+(-265)^3+(-829)^3+842^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{23^3+170^3+905^3+(-907)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{77^3+575^3+833^3+(-916)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-379)^3+704^3+788^3+(-922)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{197^3+650^3+842^3+(-958)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{176^3+(-202)^3+(-964)^3+965^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{71^3+176^3+983^3+(-985)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{176^3+(-811)^3+(-904)^3+1082^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{125^3+(-808)^3+(-922)^3+1094^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{68^3+869^3+926^3+(-1132)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-226)^3+926^3+974^3+(-1195)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{(-655)^3+(-796)^3+(-979)^3+1199^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~\bbox[3px,border:1px green solid]{662^3+872^3+965^3+(-1228)^3}\mathbf{\color{blue}{\;=\;}}\)

\(\qquad~~~~(z\gt1000)\)

\(149\mathbf{\color{blue}{\;=\;}}\)(som van vijf vijfdemachten)

\(\qquad~~~~\)(fully searched up to \(z=1000)\)

\(\qquad~~~~\bbox[lightyellow,3px,border:1px blue solid]{~oplossing~onbekend~}\mathbf{\color{blue}{\;=\;}}\)

149.2

\(149^2\mathbf{\color{blue}{\;=\;}}51^2+140^2~~\) (enige oplossing met limieten grondtal \(9999\) en exponent \(19\) )

\(149^3\mathbf{\color{blue}{\;=\;}}470^2+1757^2\mathbf{\color{blue}{\;=\;}}1043^2+1490^2\mathbf{\color{blue}{\;=\;}}\ldots\mathbf{\color{blue}{\;=\;}}\bbox[2px,border:1px brown dashed]{11175^2-11026^2}\)

149.3

Met de cijfers \(1,4,9\) kan men \(4\) kwadraten maken : \(1,4,9,49\) (zie ook )

149.4
Met de cijfers \(1,4,9\) kan men \(6\) priemgetallen maken : \(19,41,{\color{blue}{149}},419,491,941\) 149.5

De eerste keer dat er \(149\) opeenvolgende samengestelde getallen voorkomen gebeurt tussen de priemgetallen \(13626257\)
en \(13626407\) met aldus een priemkloof van \(150\,.~~\) (OEIS A000101.pdf)

149.6
\(149\) als resultaat met breuken waarin de cijfers van \(0\) tot \(9\) exact één keer voorkomen : (\(9\) oplossingen) :
\(237804/1596=253896/1704=378609/2541=387549/2601=401853/2697=\) \(457281/3069=475608/3192=476502/3198=792084/5316=149\) 		149.7
\(149\) is de samenvoeging van de eerste drie positieve kwadraten. 149.8
\(149\) is het kleinste getal wiens kwadraat begint met drie identieke cijfers : \(149^2={\color{indianred}{222}}01\). 149.9
Men moet \(149\) tot minimaal de \(55122\)ste macht verheffen opdat in de decimale expansie exact \(149\) \(149\)'s verschijnen.
Terloops : \(149\)\(^{55122}\) heeft een lengte van \(119791\) cijfers.
149.10

\(149\) heeft \(3\) maal het cijfer \(2\) in de decimale expansie van zijn kwadraat \(149^2=22201\).

Hier zijn de kleinste waarden voor \(k\) maal het cijfer \(2\)   (OEIS A048347) : \begin{align} 5^2&={\color{red}{2}}5\\ 15^2&={\color{red}{22}}5\\ {\color{blue}{149}}^2&={\color{red}{222}}01\\ 1415^2&={\color{red}{2}}00{\color{red}{222}}5\\ 4585^2&={\color{red}{2}}10{\color{red}{2222}}5\\ 14585^2&={\color{red}{2}}1{\color{red}{2}}7{\color{red}{2222}}5\\ 105935^2&=11{\color{red}{22222}}4{\color{red}{22}}5\\ 364585^2&=13{\color{red}{2}}9{\color{red}{2222222}}5 \end{align}

149.11

\(b\mathbf{\color{blue}{\;=\;}}149\to b\)\(^{4}\)\(+b\)\(^{8}\)\(+b\)\(^{7}\)\(+b\)\(^{5}\)\(+b\)\(^{2}\)\(+b\)\(^{2}\)\(+b\)\(^{4}\)\(+b\)\(^{6}\)\(+b\)\(^{2}\)\(+b\)\(^{4}\)\(+b\)\(^{2}\)\(+b\)\(^{4}\)\(+b\)\(^{2}\)\(+b\)\(^{8}\)\(+b\)\(^{1}\)\(+b\)\(^{0}\)\(+b\)\(^{6}\)\(+b\)\(^{2}\)\(\mathbf{\color{blue}{\;=\;}}487522462424281062~~\)
(OEIS A236067)

149.12

 ○–○–○ 

\(149^2=22201~~\) en \(~~222-prime((prime(0!)\)^^\(1))=149\)
\(149^3=3307949~~\) en \(~~?=149\)
\(149^4=492884401~~\) en \(~~?=149\)
\(149^5=73439775749~~\) en \(~~?=149\)
\(149^6=10942526586601~~\) en \(~~?=149\)
\(149^7=1630436461403549~~\) en \(~~?=149\)
\(149^8=242935032749128801~~\) en \(~~?=149\)
\(149^9=36197319879620191349~~\) en \(~~?=149\) 		149.13

Som Der Cijfers (\(sdc\)) van \(k^{\large{149}}\) is gelijk aan het grondtal \(k\). De triviale oplossingen \(0\) en \(1\) negerend vinden we :

\(\qquad\qquad~sdc\left(2206^{\large{149}}\right)=2206\qquad\qquad~sdc\left(2258^{\large{149}}\right)=2258\)

149.14

Expressie met tweemaal de cijfers uit het getal \(149\) enkel met operatoren \(+,-,*,/,()\)
\(149\mathbf{\color{blue}{\;=\;}}(4*9-1)*1*4+9\)

149.15

Als expressie met enkelcijferige toepassing, resp. van \(1\) tot \(9~~\) (met dank aan Inder. J. Taneja).
\(\qquad\qquad149=(11+1)^{(1+1)}+1+1+1+1+1\)
\(\qquad\qquad149=(2+22/2)^2-22+2\)
\(\qquad\qquad149=(33*3^3+3)/(3+3)\)
\(\qquad\qquad149=4^4+4-444/4\)
\(\qquad\qquad149=5*(5*5+5)-5/5\)
\(\qquad\qquad149=(6+6)*(6+6)+6-6/6\)
\(\qquad\qquad149=7*(7+7+7)+(7+7)/7\)
\(\qquad\qquad149=88+8*8+8-88/8\)
\(\qquad\qquad149=9*(9+9)-(99+9+9)/9\)

149.16

Met de cijfers van \(1\) tot \(9\) in stijgende en dalende volgorde (met dank aan Inder. J. Taneja) :
\(\qquad\qquad149=1+23+4+56+7*8+9\)
\(\qquad\qquad149=9+8*7+6+54+3+21\)

149.17

Het omgekeerde van \(5^{149}\) is een priemgetal.

\(\small{521302851212638818366841060685862801979883828607571775156781491620821316199823859273290707184234648921041}\)

Pari/GP code : isprime(fromdigits(Vecrev(digits(5^149))))\(\to1=\) true

(OEIS A058993)

149.18
Het kleinste getal dat exact \(149\) delers heeft is \(356811923176489970264571492362373784095686656=2^{148}\).
(OEIS A005179) 		149.19

(vier multigrades) \(149\to149^5\to\)

\begin{aligned} 149^1&=108^1-243^1+293^1+404^1-413^1\\ 149^5&=108^5-243^5+293^5+404^5-413^5\\ \\ 149^1&=336^1+389^1-592^1-921^1+937^1\\ 149^5&=336^5+389^5-592^5-921^5+937^5\\ \\ 149^1&=13^1-561^1+731^1+957^1-991^1\\ 149^5&=13^5-561^5+731^5+957^5-991^5\\ \\ 149^1&=206^1+796^1-876^1-1131^1+1154^1\\ 149^5&=206^5+796^5-876^5-1131^5+1154^5\\ \end{aligned}

149.20

Kleinste oplossing voor de positieve Pell vergelijking \(x^2-D*y^2\mathbf{\color{blue}{\;=\;}}1~\) met \(D\mathbf{\color{blue}{\;=\;}}149\).

Als \(D\) een kwadraat is dan zijn er geen oplossingen.

\(\qquad{\color{darkviolet}{25801741449}}^2-149*{\color{darkviolet}{2113761020}}^2\mathbf{\color{blue}{\;=\;}}1\)

(Pell equation solver)

149.21
De reciprook van \(149\) heeft als decimale periode de maximale waarde \(DP(1/149)\mathbf{\color{blue}{\;=\;}}149-1\mathbf{\color{blue}{\;=\;}}148\).
De volledige decimale expansie van \(1\) periode na de komma is
\(00671140939597315436241610738255033557046979865771812080536912751677852348{\color{darkcyan}{9932885906040268}}\)
\({\color{darkcyan}{4563758389261744966442953020134228187919463087248322147651}}\)

(OEIS A001913)

Splitst men deze periode van \(148\) cijfers in twee gelijke groepen van \(74\) cijfers dan is de som van elk tweetal cijfers
onder elkaar steeds \(9\).

149.22
Schakelaar
\(\mathbf[0\gets\to1000\mathbf]\)
“Allemaal Getallen”

⏮

⯬

⏴

⏵

⯮

⏭

\(149\)\(_{\large\color{green}{35}}\)\(149\)\(2\)\(150\)
\(1,149\)
Priemgetal\(10010101_2\)\(95_{16}\)
   

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Toevoegingen & Bewerking & Layout door Patrick De Geest (email)
Laatste update 6 maart 2026