1,1

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

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.

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

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

Cf. A117503.

Sequence in context: A250899 A139734 A142388 * A055783 A044369 A044750

Adjacent sequences: A117501 A117502 A117503 * A117505 A117506 A117507

easy,nonn

Enoch Haga, Mar 25 2006

Corrected by R. J. Mathar, Oct 26 2006

approved