A298270 Triangular numbers that for some k are also the sum of the first k composites.

0, 10, 78, 153, 946, 177310, 450775, 13595505, 150988753, 4478601403, 5409300078, 5589152128, 76060335351, 248156250265, 1793751529485, 176149383165876, 187718592284301, 233626949305596, 11362376565228270, 18886935830647605, 1943937379018997076

Offset

1,2

Links

Table of n, a(n) for n=1..21.

Example

10 is a term because 10 = 1 + 2 + 3 + 4 = 4 + 6.

Mathematica

Join[{0}, Select[Accumulate[Select[Range[10^6], CompositeQ]], OddQ[Sqrt[8#+1]]&]] (* The program generates the first 14 terms of the sequence. *) (* Harvey P. Dale, Apr 20 2024 *)

Prog

(PARI) lista(nn) = {my(s=0); forcomposite(n=0, nn, if(ispolygonal(s, 3), print1(s, ", ")); s += n; ); } \\ after Michel Marcus at A053767

Crossrefs

Intersection of A000217 and A053767.

Cf. A066527, A154587, A294174.

Sequence in context: A127536 A016201 A080618 * A082136 A153596 A316595

Adjacent sequences: A298267 A298268 A298269 * A298271 A298272 A298273

Keyword

nonn

Author

Altug Alkan, Feb 15 2018

Status

approved