cp's OEIS Frontend

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.

A019544 Squares whose digits are squares.

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%I A019544 #48 Jun 16 2025 11:35:18
%S A019544 0,1,4,9,49,100,144,400,441,900,1444,4900,9409,10000,10404,11449,
%T A019544 14400,19044,40000,40401,44100,44944,90000,144400,419904,490000,
%U A019544 491401,904401,940900,994009,1000000,1004004,1014049,1040400,1100401,1144900,1440000,1904400
%N A019544 Squares whose digits are squares.
%C A019544 Are there infinitely many terms not divisible by 100? - _Charles R Greathouse IV_, Sep 19 2012
%C A019544 Yes. For example, the squares of the type (k*10^m+1)^2, where m>0 and k = 2, 70, 970, 202470000  or  m>1 and k = 10^m-3, belong to the sequence. - _Bruno Berselli_, Jan 10 2013
%H A019544 Alois P. Heinz, <a href="/A019544/b019544.txt">Table of n, a(n) for n = 1..10000</a> (first 544 terms from Robert Israel)
%H A019544 Sylvester Smith, <a href="https://web.archive.org/web/20230824102807/https://fs.unm.edu/SYLSMITH.HTM">A Set of Conjectures on Smarandache Sequences</a>, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
%H A019544 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SmarandacheSequences.html">Smarandache Sequences</a>.
%F A019544 a(n) = A285550(n)^2. - _Alois P. Heinz_, Apr 21 2017
%p A019544 filter:= n -> convert(convert(n,base,10),set) subset {0,1,4,9}:
%p A019544 select(filter, [seq(n^2,n=0..10^5)]); # _Robert Israel_, Aug 14 2018
%t A019544 Select[Range[0,1100]^2,SubsetQ[{0, 1, 4, 9}, IntegerDigits[#]] &] (* _Stefano Spezia_, Nov 28 2024 *)
%o A019544 (Magma) [n^2: n in [0..2000] | forall{d: d in Intseq(n^2) | d in [0,1,4,9]}]; // _Bruno Berselli_, Jan 10 2013
%Y A019544 Cf. A285550.
%K A019544 nonn,base
%O A019544 1,3
%A A019544 R. Muller
%E A019544 Offset changed to 1 by _Alois P. Heinz_, Apr 21 2017