Voozh

A007960

Positive numbers k with the property that some permutation of the digits of k is a triangular number.

1, 3, 6, 10, 12, 15, 19, 21, 28, 30, 36, 45, 51, 54, 55, 60, 63, 66, 78, 82, 87, 91, 100, 102, 105, 109, 117, 120, 123, 132, 135, 136, 147, 150, 153, 156, 163, 165, 168, 171, 174, 186, 190, 201, 208, 210, 213, 231, 235, 253, 258, 267, 276, 280, 285, 300, 306, 307

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Leading zeros may be omitted from the permutation of the digits of k to get T. But the number of digits of T must be <= the number of digits of k. - N. J. A. Sloane, Dec 14 2007

Working modulo 9, A010878(A000217(j)) is in the set {0, 1, 3, 6} for all j, never in {2, 4, 5, 7, 8}. Since permutation of decimal digits does not change values mod 9, A010878(n) is also one of {0,1,3,6}. - R. J. Mathar, Jan 08 2008

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

F. Smarandache, Only Problems, Not Solutions!

EXAMPLE

Contains k=1, k=10, k=100, etc. derived from T=1.

Contains k=3, k=30, k=300, etc. derived from T=3.

Contains k=15, k=51, k=105, k=150, etc. derived from T=15.

MAPLE

q:= n-> ormap(issqr, map(x-> 1+8*parse(cat(x[])),

combinat[permute](convert(n, base, 10)))):

select(q, [$1..500])[]; # Alois P. Heinz, Aug 22 2021

MATHEMATICA