A006716 Squares with digits 1, 4, 9. (Formerly M3369)

1, 4, 9, 49, 144, 441, 1444, 11449, 44944, 991494144, 4914991449, 149991994944, 9141411499911441, 199499144494999441, 9914419419914449449, 444411911999914911441, 419994999149149944149149944191494441

Offset

1,2

Comments

This is probably a finite sequence, but that is only a conjecture.

Since 1, 4 and 9 are squares, all terms are in A053059. - Rabii Younès, Mar 17 2025

References

Elena Deza and Michel Marie Deza, Figurate numbers, World Scientific Publishing (2012), page 423.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

I. Vardi, Computational Recreations in Mathematica. Addison-Wesley, Redwood City, CA, 1991, p. 234.

Links

Table of n, a(n) for n=1..17.

Patrick De Geest, Squares containing at most three distinct digits, Index entries for related sequences

A. Ottens, The arithmetic-digits-squares-three.digits problem

Eric Weisstein's World of Mathematics, Square Number

Formula

a(n) = A027675(n)^2. - M. F. Hasler, Nov 15 2017

Crossrefs

Subsequence of A019544 and A053059.

Cf. A027675 (square roots), A061269.

For other digit groups {0,1,2} through {7,8,9}, see also: A058411, ..., A058472, A058473, A058474.

Sequence in context: A061867 A019544 A053059 * A068809 A231177 A110481

Adjacent sequences: A006713 A006714 A006715 * A006717 A006718 A006719

Keyword

nonn,base

Author

N. J. A. Sloane, revised Jul 10 2015

Extensions

a(13) corrected by Neven Juric (neven.juric(AT)apis-it.hr), May 14 2003

Status

approved