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A061380
Triangular numbers with product of digits also a triangular number.
3
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
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
MATHEMATICA
tn=Table[n (n+1)/2, {n, 0, 110}] ; Select[tn, MemberQ[tn, Times@@IntegerDigits[#]]&] (* James C. McMahon, Sep 25 2024 *)
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
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