A116911 Prime partial sums of pentagonal numbers with prime indices.

5, 17, 4957, 129277, 2826443, 3861083, 5126483, 9451573, 19811083, 53751743, 68136617, 98729003, 264616831, 388771421, 498157871, 608312141, 682548511, 779346653, 918754301, 1174179079, 1700023891, 2056298683, 2149703411

Offset

1,1

Comments

See also: A116994 Prime partial sums of triangular numbers with prime indices. A116995 Pentagonal numbers with prime indices.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

A000040 INTERSECTION {Partial sums of A116995(n)}. (Sum_{i=1..k} A000326(A000040(i))) iff in A000040. (Sum_{i=1..k} prime(i)*(3*prime(i)-1)/2) iff in A000040.

Example

a(1) = Sum_{i=1..1} prime(i)*(3*prime(i)-1)/2 = P(2) = 5.
a(2) = Sum_{i=1..2} prime(i)*(3*prime(i)-1)/2 = P(2) + P(3) = 17.
a(3) = Sum_{i=1..11} prime(i)*(3*prime(i)-1)/2 = P(2) + P(3) + P(5) + P(7) + P(11) + P(13) + P(17) + P(19) + P(23) + P(29) + P(31) = 4957.
a(4) = P(2) + ... + P(103) = 129277.

Maple

P:=n->n*(3*n-1)/2: seq(P(n), n=0..10): a:=proc(n) if isprime(sum(P(ithprime(j)), j=1..n))=true then sum(P(ithprime(j)), j=1..n) else fi end: seq(a(n), n=1..600); # Emeric Deutsch, Apr 15 2006

Mathematica

Module[{nn=4000, pn, pr}, pn=PolygonalNumber[5, Range[nn]]; pr=Table[If[ PrimeQ[ n], 1, 0], {n, nn}]; Select[Accumulate[Pick[pn, pr, 1]], PrimeQ]] (* Harvey P. Dale, Jan 27 2020 *)

Crossrefs

Cf. A000040, A000217, A034953, A085739, A116994, A116995.

Sequence in context: A085832 A062223 A363759 * A351890 A097491 A120087

Adjacent sequences: A116908 A116909 A116910 * A116912 A116913 A116914

Keyword

easy,nonn

Author

Jonathan Vos Post, Apr 03 2006

Extensions

More terms from Emeric Deutsch, Apr 15 2006

Status

approved