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A117504
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Prime at which the cumulative sum in A117503 is prime.
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3
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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
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OFFSET
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1,1
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LINKS
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FORMULA
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Multiply consecutive primes by Pi, truncate to integer, sum until a prime sum is reached.
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EXAMPLE
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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.
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MAPLE
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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
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MATHEMATICA
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Prime[#]&/@Flatten[Position[Accumulate[Table[Floor[Pi p], {p, Prime[Range[500]]}]], _?PrimeQ]] (* Harvey P. Dale, Jul 19 2023 *)
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PROG
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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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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