

A007960


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


2



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


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



