A081990 Numbers k that have no zero digits and such that both k+1 and (product of digits of k) + 1 are squares.

3, 8, 24, 35, 168, 528, 624, 783, 1443, 3843, 5183, 7568, 8835, 12543, 13224, 15128, 17423, 24335, 26243, 27224, 41615, 47523, 75624, 87615, 92415, 118335, 128163, 135423, 172224, 213443, 225624, 262143, 265224, 274575, 338723, 345743, 374543

Offset

1,1

Links

Table of n, a(n) for n=1..37.

Example

168 belongs to this sequence as both 1*6*8 + 1 = 49 and 168 + 1 = 169 are squares.

Mathematica

Select[Range[375000], DigitCount[#, 10, 0]==0&&AllTrue[{Sqrt[#+1], Sqrt[Times@@IntegerDigits[#]+1]}, IntegerQ]&] (* Harvey P. Dale, Nov 10 2025 *)

Crossrefs

Cf. A081989.

Sequence in context: A379715 A280190 A037450 * A084920 A323278 A026556

Adjacent sequences: A081987 A081988 A081989 * A081991 A081992 A081993

Keyword

base,easy,nonn

Author

Amarnath Murthy, Apr 04 2003

Extensions

Corrected and extended by Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 06 2003

Definition modified and clarified by Harvey P. Dale, Nov 10 2025

Status

approved