A006716 Squares with digits 1, 4, 9.

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

Offset: 1

Author

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

Keywords

• nonn
• base

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

• 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

• 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

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.

Formula

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

Extensions

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