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

1,1

Links

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

Formula

A000040 INTERSECTION {A085739 Partial sums of A034953(n)}. Primes in A085739. (Sum_{i=1..k} A000217(A000040(i))) iff in A000040. (Sum_{i=1..k} (A000040(i)*(A000040(i)+1)/2) iff in A000040.

Example

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.

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 *)

Crossrefs

Cf. A000040, A000217, A034953, A085739.

Sequence in context: A262652 A262500 A290944 * A367542 A172940 A096730

Adjacent sequences: A116991 A116992 A116993 * A116995 A116996 A116997

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 02 2006

Extensions

More terms from Emeric Deutsch, Apr 06 2006

Status

approved