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%I #19 Apr 22 2025 18:45:47
%S 1,7,44,888,5555,88888,1111111,2222222,22222222,77777777,1111111111,
%T 7777777777,22222222222,44444444444,444444444444,1111111111111,
%U 4444444444444,7777777777777,999999999999999,7777777777777777,22222222222222222,77777777777777777
%N Happy repdigit numbers.
%H Shyam Sunder Gupta, <a href="https://doi.org/10.1007/978-981-97-2465-9_7">Happy Numbers</a>, Exploring the Beauty of Fascinating Numbers, Springer (2025) Ch. 7, 209-222.
%e 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).
%t 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 *)
%Y Intersection of A010785 and A007770.
%K nonn,base
%O 1,2
%A _Shyam Sunder Gupta_, Apr 14 2025