World!Of
Numbers  WON plate
83 |

Repdigits, or numbers with repeated digits

For repdigit 22 see WONplate 32 For repdigit 55 see WONplate 81 The repdigit 77 can be written as the sum of three squared consecutives
42 + 52 + 62 The repdigit 88 can be written as the sum of four consecutive primes
17 + 19 + 23 + 29 The repdigit 222 can be expressed as the sum of just two consecutive primes
109 + 113 The repdigit 1111 can be the result of various transformations of the prime 11
1. Concatenate 11 with itself.
2. Multiply 11 by 101.
3. ...
But the most extraordinary way must surely be this one :
 112 + 122 + 132 + 142 + 152 + 162 = 1111
In borderprime world 1111 occurs a few time as displacement value

10731 + 1111
101512 + 1111
101787 + 1111
102146 + 1111
103987 + 1111
104056 + 1111
105296 + 1111

So far only these 7 positive displacements have been discovered ! The repdigit 8888 can be expressed as the sum of just two consecutive primes
4441 + 4447 The following repdigits are, once converted into hexadecimal base, also palindromic !
333333 = 51615
666666 = A2C2A The repdigit number 777777 can be expressed as the sum of three consecutive primes
259229 + 259271 + 259277 Two repdigit numbers of the form (4)n can be expressed as the sum
of the squares of consecutive numbers (#8 and #63 resp.)
n = 5 44444 712 + 722 + ... + 772 + 782
n = 6 444444 512 + 522 + ... + 1122 + 1132 A010785 Repdigit numbers, or numbers with repeated digits. - N. J. A. Sloane
A028987 Repdigit - 1 is prime (next term is 88...8 (72 digits)). - Patrick De Geest
A028988 Repdigit + 1 is prime (next term is 22...2 (36 digits)). - Patrick De Geest  A000083 Prime Curios! Prime Puzzle  Wikipedia 83 Le Nombre 83 Numberland 83 ```

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Patrick De Geest - Belgium - Short Bio - Some Pictures