A019544 Squares whose digits are squares.

0, 1, 4, 9, 49, 100, 144, 400, 441, 900, 1444, 4900, 9409, 10000, 10404, 11449, 14400, 19044, 40000, 40401, 44100, 44944, 90000, 144400, 419904, 490000, 491401, 904401, 940900, 994009, 1000000, 1004004, 1014049, 1040400, 1100401, 1144900, 1440000, 1904400

Offset: 1

Author

R. Muller

Keywords

• nonn
• base

Comments

Are there infinitely many terms not divisible by 100? - Charles R Greathouse IV, Sep 19 2012

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000 (first 544 terms from Robert Israel)
• Sylvester Smith, A Set of Conjectures on Smarandache Sequences, Bulletin of Pure and Applied Sciences, (Bombay, India), Vol. 15 E (No. 1), 1996, pp. 101-107.
• Eric Weisstein's World of Mathematics, Smarandache Sequences.

Crossrefs

Cf. A285550.

Programs

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

Maple

filter:= n -> convert(convert(n,base,10),set) subset {0,1,4,9}:
select(filter, [seq(n^2,n=0..10^5)]); # Robert Israel, Aug 14 2018

Mathematica

Select[Range[0,1100]^2,SubsetQ[{0, 1, 4, 9}, IntegerDigits[#]] &] (* Stefano Spezia, Nov 28 2024 *)

Formula

a(n) = A285550(n)^2. - Alois P. Heinz, Apr 21 2017

Extensions

Offset changed to 1 by Alois P. Heinz, Apr 21 2017