A116994 Prime partial sums of triangular numbers with prime indices.

3, 1759, 3323, 469303, 605113, 641969, 1110587, 1426669, 11148289, 18352349, 20473721, 21820391, 24710753, 30048589, 36690923, 40785301, 97060681, 155135369, 160593239, 168132247, 361391623, 377965069, 416572171, 645803201

Offset: 1

Author

Jonathan Vos Post, Apr 02 2006

Keywords

• easy
• nonn

Examples

			a(1) = Sum_{i=1..1} prime(i)*(prime(i)+1)/2 = T(2) = 3.
a(2) = Sum_{i=1..11} prime(i)*(prime(i)+1)/2 = T(2)+T(3)+T(5)+T(7)+T(11)+T(13)+T(17)+T(19)+T(23)+T(29)+T(31) = 1759.
a(3) = Sum_{i=1..13} prime(i)*(prime(i)+1)/2 = 3323.
a(4) = Sum_{i=1..53} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(241) = 469303.
a(5) = Sum_{i=1..57} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(269) = 605113.
a(6) = Sum_{i=1..58} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(271) = 641969.
a(7) = Sum_{i=1..68} prime(i)*(prime(i)+1)/2 = T(2) + ... + T(337) = 1110587.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A000040, A000217, A034953, A085739.

Programs

Maple

T:=n->n*(n+1)/2: a:=proc(n): if isprime(sum(T(ithprime(j)),j=1..n))=true then sum(T(ithprime(j)),j=1..n) else fi end: seq(a(n),n=1..500); # Emeric Deutsch, Apr 06 2006

Mathematica

Select[Accumulate[Table[(n(n+1))/2,{n,Prime[Range[500]]}]],PrimeQ] (* Harvey P. Dale, Jan 25 2015 *)

Formula

A000040 INTERSECTION A085739. Primes in A085739.

Extensions

More terms from Emeric Deutsch, Apr 06 2006