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
Examples
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.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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
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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 *)
Formula
Extensions
More terms from Emeric Deutsch, Apr 15 2006
Comments