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

Author

Enoch Haga, Mar 25 2006

Keywords

• easy
• nonn

Examples

			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.
		

Crossrefs

Cf. A117503.

Programs

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 *)

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

Formula

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

Extensions

Corrected by R. J. Mathar, Oct 26 2006