A065311 Primes which occur exactly twice in the sequence of a(n) = prime(n) - prime(n - pi(n)) = A065308(n).

3, 5, 13, 17, 29, 31, 43, 67, 71, 97, 107, 109, 131, 157, 181, 191, 223, 233, 239, 269, 281, 313, 359, 379, 383, 401, 409, 431, 503, 523, 569, 571, 619, 631, 659, 691, 719, 751, 787, 797, 857, 859, 881, 883, 971, 1039, 1061, 1063, 1091, 1117, 1123, 1201

Offset: 1

Author

Labos Elemer, Oct 29 2001

Keywords

• nonn

Comments

In A065308, each odd prime seems to appear once or twice.

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A000720, A054546, A065308, A065309, A065310, A065311.

Programs

Mathematica

Most@ Select[Tally@ Array[Prime[# - PrimePi@ #] &, 300], Last@ # == 2 &][[All, 1]] (* Michael De Vlieger, Nov 03 2017 *)

PARI

{ n=0; p=1; f=2; m=1; for (i=1, 10^9, a=0; p=nextprime(p + 1); while (p==f, a++; m++; f=prime(m - primepi(m))); if (a==2, write("b065311.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 16 2009