A364799 Triangular numbers that for some k >= 1 are also the sum of the first k odd primes.

3, 15, 1236378, 1454365, 3541791, 104856921, 2677839153, 3656187921870, 3973810409128, 1448587865213374600, 36691639282445615088081

Offset: 1

Author

Ilya Gutkovskiy, Aug 08 2023

Keywords

• nonn
• more

Comments

a(n) = A000217(i) = A071148(j) for appropriate i, j.

Examples

			15 is a term because 15 = 1 + 2 + 3 + 4 + 5 = 3 + 5 + 7.
		

Crossrefs

Intersection of A000217 and A071148.

Cf. A065091, A066527, A364798.

Programs

Mathematica

Select[Accumulate[Prime[Range[2, 1000000]]], IntegerQ[Sqrt[8 # + 1]] &]

PARI

lista(nn) = my(s=0); forprime(p=3, nn, s+=p; if(ispolygonal(s, 3), print1(s, ", "))) \\ Jinyuan Wang, Aug 10 2023

Extensions

a(10) from Jinyuan Wang, Aug 10 2023

a(11) from Martin Ehrenstein, Aug 23 2023