A381046 Happy repdigit numbers.

1, 7, 44, 888, 5555, 88888, 1111111, 2222222, 22222222, 77777777, 1111111111, 7777777777, 22222222222, 44444444444, 444444444444, 1111111111111, 4444444444444, 7777777777777, 999999999999999, 7777777777777777, 22222222222222222, 77777777777777777

Offset

1,2

Links

Table of n, a(n) for n=1..22.

Shyam Sunder Gupta, Happy Numbers, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 7, 209-222.

Example

888 is a term since it is a repdigit number consisting of digit 8 only and is also a happy number (64+64+64 = 192, and 1+81+4 = 86, and 64+36 = 100, and 1+0+0 = 1).

Mathematica

happyQ[n_] := NestWhile[Total[IntegerDigits[#]^2] &, n, UnsameQ, All] == 1; Select[Union[Table[k*(10^n - 1)/9, {k, 1, 9}, {n, 17}] // Flatten], happyQ] (* Amiram Eldar, Apr 14 2025 *)

Crossrefs

Intersection of A010785 and A007770.

Sequence in context: A166775 A221541 A327680 * A156374 A171493 A262772

Adjacent sequences: A381043 A381044 A381045 * A381047 A381048 A381049

Keyword

nonn,base

Author

Shyam Sunder Gupta, Apr 14 2025

Status

approved