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

1,3

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

Robert Israel, Table of n, a(n) for n = 1..544

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

Formula

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

Maple

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

Prog

(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

Crossrefs

Cf. A285550.

Sequence in context: A368337 A268099 A061867 * A053059 A006716 A068809

Adjacent sequences: A019541 A019542 A019543 * A019545 A019546 A019547

Keyword

nonn,base

Author

R. Muller

Extensions

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

Status

approved