A271629 Squares that are the sum of the digits of the numbers from 0 to n, for some n.

0, 1, 36, 81, 100, 144, 289, 441, 784, 900, 1225, 1296, 3025, 3600, 5041, 5625, 6400, 8100, 8649, 10000, 11881, 15625, 15876, 18225, 23716, 36100, 41616, 44100, 50625, 55225, 57600, 62001, 67600, 72900, 78400, 99225, 122500, 129600, 136900, 145161, 168921, 189225

Offset

1,3

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Example

0 = 0^2; 1 = 1^2; 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36 = 6^2.

Maple

with(numtheory): P:=proc(q) local a, b, c, k, n; a:=0; for n from 0 to q do b:=0; c:=n;
for k from 1 to ilog10(n)+1 do b:=b+(c mod 10); c:=trunc(c/10); od; a:=a+b;
if a=trunc(sqrt(a))*trunc(sqrt(a)) then print(a); fi; od; end: P(10^6);

Mathematica

Select[Accumulate@ Map[Total@ IntegerDigits@ # &, Range[0, 10^4]], IntegerQ@ Sqrt@ # &] (* Michael De Vlieger, Apr 11 2016 *)

Prog

(PARI) lista(nn) = for (n=0, nn, if (issquare(s=sum(k=1, n, sumdigits(k))), print1(s, ", "))); \\ Michel Marcus, Apr 11 2016

Crossrefs

Cf. A037123, A271626.

Sequence in context: A286430 A279901 A335276 * A171675 A136359 A257649

Adjacent sequences: A271626 A271627 A271628 * A271630 A271631 A271632

Keyword

nonn,easy,base

Author

Paolo P. Lava, Apr 11 2016

Status

approved