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%I #5 Oct 23 2014 20:53:07
%S 1,5,3,15,6,30,10,50,69,21,98,28,132,36,171,45,215,55,264,66,318,78,
%T 377,91,441,105,510,120,584,136,663,153,747,817,190,910,210,1008,231,
%U 1111,253,1219,276,1332,300,1450,325,1573,351,1701,378,1834,406,1972,435,2115,465,2263,496
%N Sequence of distinct least positive numbers such that the average of the first n terms is a triangular number.
%e 1/1 = 1 is a triangular number. So a(1) = 1.
%e (1+2)/2 is not a triangular number. (1+3)/2 is not a triangular number. (1+4)/2 is not a triangular number. (1+5)/2 = 3 is a triangular number. So a(2) = 5.
%o (PARI) v=[]; n=1; while(n<5000, num=(vecsum(v)+n); if(num%(#v+1)==0&&vecsearch(vecsort(v), n)==0, for(i=1, n, if(i*(i+1)/2>(num/(#v+1)), break); if(i*(i+1)/2==(num/(#v+1)), print1(n, ", "); v=concat(v, n); n=1; break))); n++)
%Y Cf. A000217.
%K nonn
%O 1,2
%A _Derek Orr_, Oct 18 2014
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