A007960 - OEIS

%I #26 Dec 15 2022 14:22:31

%S 1,3,6,10,12,15,19,21,28,30,36,45,51,54,55,60,63,66,78,82,87,91,100,

%T 102,105,109,117,120,123,132,135,136,147,150,153,156,163,165,168,171,

%U 174,186,190,201,208,210,213,231,235,253,258,267,276,280,285,300,306,307

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

%C 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

%C 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

%H Alois P. Heinz, <a href="/A007960/b007960.txt">Table of n, a(n) for n = 1..10000</a>

%H F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">Only Problems, Not Solutions!</a>

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

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

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

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

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

%p select(q, [$1..500])[];  # _Alois P. Heinz_, Aug 22 2021

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

%Y Cf. A000217.

%K nonn,base

%O 1,2

%A R. Muller

%E A large number of errors corrected by _N. J. A. Sloane_, Apr 15 1996

%E Edited, corrected and extended by _R. J. Mathar_, Jan 08 2008