A065312 Primes which occur exactly once in A065308 (prime(n - pi(n))).

7, 11, 19, 23, 37, 41, 47, 53, 59, 61, 73, 79, 83, 89, 101, 103, 113, 127, 137, 139, 149, 151, 163, 167, 173, 179, 193, 197, 199, 211, 227, 229, 241, 251, 257, 263, 271, 277, 283, 293, 307, 311, 317, 331, 337, 347, 349, 353, 367, 373, 389, 397, 419, 421, 433

Offset: 1

Author

Labos Elemer, Oct 29 2001

Keywords

• nonn

Comments

In A065308 each odd prime seems to appear once or twice. Prime 2 arises there 3 times.

Links

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

Crossrefs

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

Programs

Mathematica

With[{s = Array[Prime[# - PrimePi[#]] &, 120]}, Most@ Select[Split[s], Length@ # == 1 &][[All, 1]] ] (* Michael De Vlieger, Jun 19 2018 *)

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==1, write("b065312.txt", n++, " ", p); if (n==1000, return)) ) } \\ Harry J. Smith, Oct 16 2009