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

1,2

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

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 *)

Crossrefs

Cf. A002477, A080151, A080161, A080162.

Cf. A007953.

Sequence in context: A077356 A077357 A294497 * A110723 A376215 A084617

Adjacent sequences: A080157 A080158 A080159 * A080161 A080162 A080163

Keyword

nonn,base

Author

N. J. A. Sloane, Jun 19 2005

Extensions

More terms from Emeric Deutsch, Jun 19 2005

Status

approved