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

1,2

Links

Table of n, a(n) for n=1..59.

Example

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.

Prog

(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++)

Crossrefs

Cf. A000217.

Sequence in context: A167583 A351951 A329029 * A298975 A070375 A166465

Adjacent sequences: A248980 A248981 A248982 * A248984 A248985 A248986

Keyword

nonn

Author

Derek Orr, Oct 18 2014

Status

approved