A061910 Positive numbers k such that sum of digits of k^2 is a square.

1, 2, 3, 6, 9, 10, 11, 12, 13, 14, 15, 18, 20, 21, 22, 23, 30, 31, 39, 41, 45, 48, 51, 58, 59, 60, 67, 68, 76, 77, 85, 86, 90, 94, 95, 100, 101, 102, 103, 104, 105, 110, 111, 112, 113, 120, 121, 122, 130, 131, 139, 140, 148, 150, 157, 158, 166, 175, 176, 180, 184, 185

Offset

1,2

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

MathStackExchange, Numbers n such that the digit sum of n2 is a square, 2015-2016.

Example

6^2 = 36 and 3+6 = 9 is a square. 13^2 = 169 and 1+6+9 = 16 is a square.

Maple

readlib(issqr): f := []: for n from 1 to 200 do if issqr(convert(convert(n^2, base, 10), `+`)) then f := [op(f), n] fi; od; f;

Mathematica

Select[Range[185], IntegerQ[Sqrt[Total[IntegerDigits[#^2]]]] &] (* Jayanta Basu, May 06 2013 *)

Prog

(Magma) [ n: n in [1..185] | IsSquare(&+Intseq(n^2)) ];  // Bruno Berselli, Jul 29 2011
(PARI) is(n)=n=eval(Vec(Str(n^2))); issquare(sum(i=1, #n, n[i])) \\ Charles R Greathouse IV, Jul 29 2011
(PARI) select( is_A061910(n)=issquare(sumdigits(n^2)), [0..199]) \\ Includes the initial 0. - M. F. Hasler, Oct 16 2017
(Python)
from gmpy2 import is_square
A061910 = [n for n in range(1, 10**3) if is_square(sum(int(d) for d in str(n*n)))] # Chai Wah Wu, Sep 03 2014

Crossrefs

Cf. A007953, A004159, A053057, A061909, A061911, A061912.

Sequence A293832 gives the start of the first run of n consecutive values.

Sequence in context: A097108 A140783 A094351 * A344208 A007086 A047404

Adjacent sequences: A061907 A061908 A061909 * A061911 A061912 A061913

Keyword

nonn,base

Author

Asher Auel, May 17 2001

Status

approved