cp's OEIS Frontend

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

%I A061910 #39 Mar 09 2024 11:05:40
%S A061910 1,2,3,6,9,10,11,12,13,14,15,18,20,21,22,23,30,31,39,41,45,48,51,58,
%T A061910 59,60,67,68,76,77,85,86,90,94,95,100,101,102,103,104,105,110,111,112,
%U A061910 113,120,121,122,130,131,139,140,148,150,157,158,166,175,176,180,184,185
%N A061910 Positive numbers k such that sum of digits of k^2 is a square.
%H A061910 Bruno Berselli, <a href="/A061910/b061910.txt">Table of n, a(n) for n = 1..1000</a>
%H A061910 MathStackExchange, <a href="https://math.stackexchange.com/questions/1093266/numbers-n-such-that-the-digit-sum-of-n2-is-a-square/2258657">Numbers n such that the digit sum of n2 is a square</a>, 2015-2016.
%e A061910 6^2 = 36 and 3+6 = 9 is a square. 13^2 = 169 and 1+6+9 = 16 is a square.
%p A061910 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;
%t A061910 Select[Range[185], IntegerQ[Sqrt[Total[IntegerDigits[#^2]]]] &] (* _Jayanta Basu_, May 06 2013 *)
%o A061910 (Magma) [ n: n in [1..185] | IsSquare(&+Intseq(n^2)) ];  // _Bruno Berselli_, Jul 29 2011
%o A061910 (PARI) is(n)=n=eval(Vec(Str(n^2)));issquare(sum(i=1,#n,n[i])) \\ _Charles R Greathouse IV_, Jul 29 2011
%o A061910 (PARI) select( is_A061910(n)=issquare(sumdigits(n^2)), [0..199]) \\ Includes the initial 0. - _M. F. Hasler_, Oct 16 2017
%o A061910 (Python)
%o A061910 from gmpy2 import is_square
%o A061910 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
%Y A061910 Cf. A007953, A004159, A053057, A061909, A061911, A061912.
%Y A061910 Sequence A293832 gives the start of the first run of n consecutive values.
%K A061910 nonn,base
%O A061910 1,2
%A A061910 _Asher Auel_, May 17 2001