A080160 Squares that are digit sums of Wonderful Demlo numbers A002477.

1, 4, 9, 16, 25, 36, 49, 64, 81, 324, 441, 576, 729, 900, 1089, 1296, 2025, 2304, 2601, 2916, 3249, 3600, 3969, 5184, 5329, 5476, 5625, 5776, 5929, 6084, 6241, 6400, 6561, 6724, 6889, 7056, 7225, 7396, 7569, 7744, 7921, 8100, 9801, 10404, 11025, 11664

Offset: 1

Author

N. J. A. Sloane, Jun 19 2005

Keywords

• nonn
• base

Comments

These are the squares in A080151.

x^2 is a term iff x mod 81 is in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 18, 21, 24, 27, 30, 33, 36, 45, 48, 51, 54, 57, 60, 63, 72, 73, 74, 75, 76, 77, 78, 79, 80}. - Robert Israel, Jul 30 2025

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Demlo Number

Crossrefs

Cf. A002477, A080151, A080161, A080162.

Cf. A007953.

Programs

Maple

b:=n->sum(convert(((10^(n+1)-1)/9)^2,base,10)[j],j=1..2*n+1): a:=proc(n) if type(sqrt(b(n)),integer)=true then b(n) else fi end: seq(a(n),n=0..2000); # Emeric Deutsch, Jun 19 2005

Mathematica

A080151[n_] := (9^2)*(n/9 - FractionalPart[n/9] + FractionalPart[n/9]^2)
A080151[Select[Range[10000], IntegerQ[Sqrt[A080151[#]]] &]]
(* Enrique Pérez Herrero, Nov 05 2022 *)

Extensions

More terms from Emeric Deutsch, Jun 19 2005