A061380 Triangular numbers with product of digits also a triangular number.

0, 1, 3, 6, 10, 66, 105, 120, 153, 190, 210, 231, 300, 351, 406, 465, 630, 703, 741, 780, 820, 903, 990, 1035, 1081, 1326, 1540, 1770, 1830, 2016, 2080, 2556, 2701, 2850, 3003, 3081, 3160, 3240, 3403, 3570, 4005, 4095, 4560, 4950, 5050, 5460, 5671, 6105

Offset

1,3

Links

Table of n, a(n) for n=1..48.

Example

153 is a triangular number and the product of digits 15 is also a triangular number.

Maple

q:= n-> (l-> issqr(1+8*mul(i, i=l)))(convert(n, base, 10)):
select(q, [seq(i*(i+1)/2, i=0..110)])[];  # Alois P. Heinz, Mar 17 2023

Prog

(Magma) [t: n in [0..110] | IsSquare(8*p+1) where p is &*Intseq(t) where t is (n*(n+1) div 2)];  // Bruno Berselli, Jun 30 2011
(PARI) isok(k) = ispolygonal(k, 3) && ispolygonal(vecprod(digits(k)), 3); \\ Michel Marcus, Mar 17 2023

Crossrefs

Cf. A000217.

Sequence in context: A071299 A338767 A351131 * A350993 A308849 A354000

Adjacent sequences: A061377 A061378 A061379 * A061381 A061382 A061383

Keyword

nonn,base,easy

Author

Amarnath Murthy, May 02 2001

Extensions

More terms from Erich Friedman, May 08 2001

Offset 1 from Michel Marcus, Mar 17 2023

Status

approved