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%I #13 Apr 21 2024 11:38:36
%S 37,137,151,173,409,467,503,677,937,1091,1153,1229,1303,1409,1453,
%T 1471,1531,2137,2221,2251,2393,2503,2593,2633,2671,2797,2837,3001,
%U 3023,3089,3163
%N Prime at which the cumulative sum in A117503 is prime.
%F Multiply consecutive primes by Pi, truncate to integer, sum until a prime sum is reached.
%e 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.
%p 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_
%t Prime[#]&/@Flatten[Position[Accumulate[Table[Floor[Pi p],{p,Prime[Range[500]]}]],_?PrimeQ]] (* _Harvey P. Dale_, Jul 19 2023 *)
%o (UBASIC)
%o 10 Ct=1
%o 20 B=nxtprm(B)
%o 30 C=int(pi(B))
%o 40 D=D+C
%o 41 print Ct,B,C,D
%o 50 if D=prmdiv(D) then print D:stop
%o 55 Ct=Ct+1
%o 60 goto 20
%Y Cf. A117503.
%K easy,nonn,changed
%O 1,1
%A _Enoch Haga_, Mar 25 2006
%E Corrected by _R. J. Mathar_, Oct 26 2006
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