This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053057 #80 Jul 02 2025 16:01:59
%S A053057 0,1,4,9,36,81,100,121,144,169,196,225,324,400,441,484,529,900,961,
%T A053057 1521,1681,2025,2304,2601,3364,3481,3600,4489,4624,5776,5929,7225,
%U A053057 7396,8100,8836,9025,10000,10201,10404,10609,10816,11025,12100,12321,12544,12769
%N A053057 Squares whose digit sum is also a square.
%C A053057 The numbers 81, 100, 121, 144, 169, 196, 225 are seven consecutive squares belonging to this sequence. The next set of seven consecutive squares whose digit sum is also a square is {9999^2, 10000^2, 10001^2, 10002^2, 10003^2, 10004^2, 10005^2}. (See Crux Mathematicorum link.) - _Bernard Schott_, May 24 2017
%C A053057 The first set of 8 consecutive squares begin at 46045846^2. This was already known in 2016, see MathStackExchange link. - _Michel Marcus_, May 25 2017
%C A053057 The first run of 9 consecutive squares starts at 302260461719025^2. - _Giovanni Resta_, Jun 08 2017
%D A053057 Felice Russo, A set of new Smarandache functions, sequences and conjectures in number theory, American Research Press, 2000.
%H A053057 Daniel Mondot, <a href="/A053057/b053057.txt">Table of n, a(n) for n = 1..1192</a>
%H A053057 Allan Wm. Johnson Jr., <a href="https://cms.math.ca/wp-content/uploads/crux-pdfs/Crux_v6n03_Mar.pdf">Problem 443</a>, Crux Mathematicorum, Vol. 6, No. 3 (Mar. 1980), page 88.
%H A053057 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 n^2 is a square</a>, 2015-2016.
%e A053057 144 is a term: 144 = 12^2 and 1 + 4 + 4 = 9 = 3^2. - _Bernard Schott_, May 24 2017
%t A053057 Select[Range[0,115]^2, IntegerQ[Sqrt[DigitSum[#]]]&] (* _Stefano Spezia_, Mar 07 2024 *)
%o A053057 (Magma) [n^2: n in [0..120] | IsSquare(&+Intseq(n^2))]; // _Bruno Berselli_, May 26 2011
%o A053057 (PARI) lista(nn) = for (n=1, nn, if (issquare(sumdigits(n^2)), print1(n^2, ", "));); \\ _Michel Marcus_, May 25 2017
%Y A053057 Subsequence of A000290.
%Y A053057 Cf. A028839, A061910.
%K A053057 nonn,easy,base
%O A053057 1,3
%A A053057 _Felice Russo_, Feb 25 2000
%E A053057 More terms from _James Sellers_, Feb 28 2000