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%I #10 Feb 23 2015 23:20:20
%S 1,2,3,4,5,6,7,8,9,22,35,49,53,56,65,69,94,96,111,123,132,136,144,163,
%T 199,213,225,231,233,238,245,252,254,266,283,312,316,321,323,328,332,
%U 355,359,361,367,376,382,388,395,414,425,441,452,477,489,498,522,524,535,539,542,553,555,558,585,593,599,613,626,631
%N Zeroless numbers n with digits d_1, d_2, ..., d_k such that d_1*(d_1+1)/2 + ... + d_k*(d_k+1)/2 is a triangular number.
%C Any one of these terms can have an arbitrary number of 0's in between any two digits. Thus, the numbers with 0's have been omitted as trivial.
%o (PARI) istri(n)=for(k=0,n+1,if(k*(k+1)/2==n,return(1)));0
%o for(n=1,10^3,d=digits(n);if(vecsort(d,,8)[1],s=0;for(i=1,#d,s+=d[i]*(d[i]+1)/2);if(istri(s),print1(n,", "))))
%Y Cf. A000217.
%K nonn,base
%O 1,2
%A _Derek Orr_, Feb 11 2015