A102351 Let p = prime(n); then a(n) = number of residues p mod q which are prime, as q runs through the primes less than p.

0, 0, 1, 1, 1, 2, 3, 2, 3, 3, 3, 4, 4, 3, 5, 4, 5, 3, 3, 5, 6, 6, 4, 7, 6, 5, 6, 6, 6, 8, 6, 7, 9, 6, 8, 6, 8, 9, 6, 7, 8, 9, 8, 10, 10, 7, 8, 8, 7, 9, 11, 11, 11, 10, 10, 9, 10, 10, 13, 11, 11, 12, 11, 12, 12, 11, 9, 11, 11, 10, 12, 15, 13, 14, 13, 13, 12, 12, 16, 14, 14, 12, 14, 14, 15, 14, 15

Offset

1,6

Comments

Number of prime prime residues of the n-th prime.

Links

Table of n, a(n) for n=1..87.

Carlos Rivera, Prime Puzzle 301

Example

a(6)=2: the 6th prime is 13. 13 mod 2 = 1; 13 mod 3 = 1; 13 mod 5 = 3 (prime); 13 mod 7 = 6; 13 mod 11 = 2 (prime).

Mathematica

f[n_] := Length[ Select[ Mod[ Prime[n], Prime[ Range[n]]], PrimeQ[ # ] &]]; Table[ f[n], {n, 87}] (* Robert G. Wilson v, Feb 22 2005 *)

Crossrefs

Cf. A102854.

Sequence in context: A346643 A272979 A357610 * A078173 A248005 A129759

Adjacent sequences: A102348 A102349 A102350 * A102352 A102353 A102354

Keyword

nonn

Author

Ray G. Opao, Feb 21 2005

Extensions

More terms from Robert G. Wilson v, Feb 22 2005

Status

approved