A092065 Numbers m such that numerator of Sum_{k=1..m} 1/(prime(k)-k) is prime.

2, 3, 4, 5, 7, 14, 21, 22, 26, 27, 32, 43, 51, 58, 62, 65, 82, 131, 148, 207, 229, 249, 257, 320, 334, 386, 423, 440, 481, 747, 823, 1181, 1314, 1915, 2025, 2269, 2700, 2717, 2801, 2865, 4548, 6015, 6364, 8532, 10612, 10863, 11960, 15156, 15898, 19186, 19622, 22203, 25345

Offset: 1

Author

Mohammed Bouayoun (mohammed.bouayoun(AT)sanef.com), Feb 20 2004; corrected Apr 24 2006

Keywords

• nonn

Comments

Note that the definition here is subtly different from that of A092063.

Crossrefs

Cf. A092066.

Programs

Maple

count:= 0:
S:= 0: p:= 0;
for n from 1 to 2500 do
  p:= nextprime(p);
  S:= S + 1/(p - n);
  if isprime(numer(S)) then
    count:= count+1;
    A[count]:= n;
  fi
od:
seq(A[i],i=1..count); # Robert Israel, Sep 07 2014

Mathematica

f=0; Do[ p=Prime[n]; f=f+1/(p-n); g=Numerator[f]; If[ PrimeQ[g], Print[n]], {n,1,500} ]

PARI

S=1;for(n=2,100,S=S+1/(prime(n)-n);if(isprime(numerator(S)),print1(n,","))) \\ Edward Jiang, Sep 08 2014

Extensions

Sequence and Mathematica program corrected by Alexander Adamchuk, Jul 29 2007

a(30)-a(34) from Vincenzo Librandi, Nov 26 2012

a(35)-a(36) from Robert Israel, Sep 07 2014

a(37)-a(53) from Michael S. Branicky, Aug 26 2024