\(149=74+75\) (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)

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

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

\(149=9^2+10^2-2^5\)

\(149=2^2+2^6+3^4\)

\(149=14*9+14+9\)

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

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)

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

149.2
Met de cijfers \(1,4,9\) kan men \(6\) priemgetallen maken : \(19,41,149,419,491,941\) 149.3

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

149.4

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

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

149.5

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

\(\Huge\bbox[border:0]{⏮}\)

\(\Huge\bbox[border:0]{⯬}\)

\(\Huge\bbox[border:0]{⏴}\)

\(\Huge\bbox[border:0]{⏵}\)

\(\Huge\bbox[border:0]{⯮}\)

\(\Huge\bbox[border:0]{⏭}\)

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

Uit de collectie 'Allemaal Getallen' van Ir. Jos Heynderickx
Toevoegingen & Bewerking & Layout door Patrick De Geest (email)
Laatste update 11 november 2024