A175133 Sum of first a(n) consecutive primes gives a triangular number.

3, 5, 217, 1065, 93448, 39545957, 240439822, 1894541497, 132563927578, 309101198255

Offset: 1

Author

Ctibor O. Zizka, Feb 20 2010

Keywords

• nonn
• more

Comments

A007504(a(n)) = A000217(j) for some j.

Numbers k such that Sum_{i=1..k} prime(i) = j*(j+1)/2, where prime(i) is i-th prime, and j an integer.

Examples

			k=3 is a term: 2+3+5=10, and 10=4*5/2 is a triangular number, j=4.
k=5 is a term: 2+3+5+7+11=28, and 28=7*8/2 is a triangular number, j=7.
k=217 is a term: 2+3+...+1327=133386, and 133386=516*517/2 is a triangular number, j=516.
		

Crossrefs

Cf. A000040, A000217, A007504, A066527.

Cf. also A033997, A364696, A366270.

Programs

PARI

isok(n) = ispolygonal(sum(k=1, n, prime(k)), 3); \\ Michel Marcus, Oct 13 2018

Extensions

a(6)-a(10) from Nathaniel Johnston, May 10 2011 (a(7)-a(10) based on comments by Donovan Johnson)

Name, comment and example clarified by Ilya Gutkovskiy, Aug 07 2023