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

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

Select[Range[500], Length[Select[FromDigits/@Permutations[ IntegerDigits[#]], IntegerQ[(Sqrt[1+8#]-1)/2]&]]>0&]  (* Marco Ripà, Nov 07 2022 *)

Crossrefs

Cf. A000217.

Sequence in context: A114981 A319452 A187744 * A339213 A280243 A032732

Adjacent sequences: A007957 A007958 A007959 * A007961 A007962 A007963

Keyword

nonn,base

Author

R. Muller

Extensions

A large number of errors corrected by N. J. A. Sloane, Apr 15 1996

Edited, corrected and extended by R. J. Mathar, Jan 08 2008

Status

approved