A117504 -id:A117504 - cp's OEIS frontend

A117503 Primes among partial sums of floor(Pi*prime(k)), k=1,2,3,....

613, 6229, 7607, 9679, 46133, 61469, 69191, 120067, 211663, 285049, 316697, 354323, 402371, 444979, 481109, 490313, 532709, 993907, 1055543, 1083721, 1237487, 1329701, 1409977, 1442899, 1484671, 1656199, 1700471, 1874767

Offset: 1

Enoch Haga, Mar 25 2006

Modeled on the same concept as cumulative sums of squared primes in A098562.

Cf. A117504, A098562.

Digits := 30 ; A117503 := 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),pisum] ; break ; fi ; od : od : RETURN(a) ; end: a := A117503(30) ; # R. J. Mathar, Oct 26 2006

Select[Accumulate[Floor[Pi Prime[Range[800]]]],PrimeQ] (* Harvey P. Dale, Jun 06 2022 *)

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

Define the sequence s as s(j) = Sum_{k=1..j} floor(Pi*prime(k)) for j >= 1; then a(n) is the n-th prime in the sequence s.

Edited by Jon E. Schoenfield, Sep 23 2018

A117528 Prime at which the cumulative sum in A117527 is prime.

Original entry on oeis.org

2, 3, 13, 41, 43, 109, 137, 167, 181, 199, 307, 373, 421, 491, 587, 661, 1009, 1097, 1117, 1373, 1471, 1483, 1601, 1607, 1787, 1913, 2053, 2089, 2203, 2267, 2591, 2819, 2953, 3191, 3361, 3623, 3691, 3779, 3877, 4051

Offset: 1

Enoch Haga, Mar 25 2006

At the twin primes 41 and 43, we obtain consecutive prime integer sums of 641 and 757.

			In a(5)=4007, multiplication of the prime 109*e resulted in the int sum 296. When added to previous sums, the total came to 4007, a prime.

Cf. A117527 A117504.

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

Multiply consecutive primes by e, take integer, sum until a prime sum is reached.

cp's OEIS Frontend

A117503 Primes among partial sums of floor(Pi*prime(k)), k=1,2,3,....

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