A117503 -id:A117503 - cp's OEIS frontend

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

Enoch Haga, Mar 25 2006

			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.

Cf. A117503.

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 *)

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

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

Corrected by R. J. Mathar, Oct 26 2006

A117527 Cumulative sums of int(prime*e) which are primes.

Original entry on oeis.org

5, 13, 109, 641, 757, 4007, 5387, 7901, 9349, 11467, 23297, 33503, 42193, 57139, 76343, 100213, 209597, 252583, 261631, 373621, 424231, 432287, 503593, 507961, 618593, 699427, 791489, 825389, 895243, 943837, 1212917, 1455901, 1573577

Offset: 1

Enoch Haga, Mar 25 2006

Sometimes prime integer sums occur with consecutive primes, as 1601*e and 1607*e.

			The 4th cumulative sum of integer products is 641, prime.

Cf. A117528 A117503.

Select[Accumulate[Floor[E*Prime[Range[500]]]],PrimeQ] (* Harvey P. Dale, Mar 27 2025 *)

10 Ct=1
20 B=nxtprm(B)
22 E=#e
30 C=int(B*E)
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

Beginning with the first prime, multiply by e, take integer, repeat, adding integer sums until a cumulative prime sum occurs. On the first prime, 2, the integer product is 5, prime. Continue to next integer product, add, until the next prime sum, 13.

cp's OEIS Frontend

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

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