A117504 Prime at which the cumulative sum in A117503 is prime.

37, 137, 151, 173, 409, 467, 503, 677, 937, 1091, 1153, 1229, 1303, 1409, 1453, 1471, 1531, 2137, 2221, 2251, 2393, 2503, 2593, 2633, 2671, 2797, 2837, 3001, 3023, 3089, 3163

Offset

1,1

Links

Table of n, a(n) for n=1..31.

Formula

Multiply consecutive primes by Pi, truncate to integer, sum until a prime sum is reached.

Example

In a(1)=37, the cumulative sum of primes 1-12 in A117503 has risen to 613, a prime -- 37 being the 12th prime to be multiplied by Pi, with integer of result added to previous results.

Maple

Digits := 30 ; A117504 := proc(nmax) local a, pisum, p ; a := [] ; pisum := 0 ; p :=1 ; while nops(a) <=nmax do while true do pisum := pisum+floor(Pi*ithprime(p)) ; p := p+1 ; if isprime(pisum) then a := [op(a), ithprime(p-1)] ; break ; fi ; od : od : RETURN(a) ; end: a := A117504(30) ; # R. J. Mathar

Mathematica

Prime[#]&/@Flatten[Position[Accumulate[Table[Floor[Pi p], {p, Prime[Range[500]]}]], _?PrimeQ]] (* Harvey P. Dale, Jul 19 2023 *)

Prog

(UBASIC)
10 Ct=1
20 B=nxtprm(B)
30 C=int(pi(B))
40 D=D+C
41 print Ct, B, C, D
50 if D=prmdiv(D) then print D:stop
55 Ct=Ct+1
60 goto 20

Crossrefs

Cf. A117503.

Sequence in context: A250899 A139734 A142388 * A055783 A044369 A044750

Adjacent sequences: A117501 A117502 A117503 * A117505 A117506 A117507

Keyword

easy,nonn

Author

Enoch Haga, Mar 25 2006

Extensions

Corrected by R. J. Mathar, Oct 26 2006

Status

approved