A248983 Sequence of distinct least positive numbers such that the average of the first n terms is a triangular number.
1, 5, 3, 15, 6, 30, 10, 50, 69, 21, 98, 28, 132, 36, 171, 45, 215, 55, 264, 66, 318, 78, 377, 91, 441, 105, 510, 120, 584, 136, 663, 153, 747, 817, 190, 910, 210, 1008, 231, 1111, 253, 1219, 276, 1332, 300, 1450, 325, 1573, 351, 1701, 378, 1834, 406, 1972, 435, 2115, 465, 2263, 496
Offset: 1
Keywords
Examples
1/1 = 1 is a triangular number. So a(1) = 1. (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.
Crossrefs
Cf. A000217.
Programs
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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++)