A125627 Number of arithmetic progressions of primes < n-th prime.

0, 1, 3, 6, 11, 17, 23, 31, 41, 53, 67, 80, 92, 108, 126, 142, 163, 185, 204, 225, 249, 272, 299, 327, 355, 384, 414, 446, 478, 510, 546, 584, 625, 662, 702, 742, 784, 828, 872, 918, 966, 1011, 1058, 1110, 1158, 1212, 1266, 1319, 1377, 1435, 1490, 1548, 1605, 1665, 1729

Offset

1,3

Links

Table of n, a(n) for n=1..55.

Example

The a(4) = 6 arithmetic progressions are:
  (2), (2,3), (2,5), (3), (3,5), (5).
The a(5) = 11 arithmetic progressions are:
  (2), (2,3), (2,5), (2,7), (3), (3,5), (3,5,7), (3,7), (5), (5,7), (7).

Prog

(PARI) apc(v)={#v + sum(i=1, #v-1, sum(j=i+1, #v, my(s=v[j]-v[i], t=v[j]+s); while(setsearch(v, t), t+=s); (t-v[j])/s))}
a(n)={apc(Set(primes(n-1)))} \\ Andrew Howroyd, Jan 29 2020

Crossrefs

Sequence in context: A034029 A310115 A310116 * A332410 A194142 A174648

Adjacent sequences: A125624 A125625 A125626 * A125628 A125629 A125630

Keyword

nonn

Author

Giovanni Teofilatto, Jan 28 2007

Extensions

a(5) corrected and terms a(7) and beyond from Andrew Howroyd, Jan 29 2020

Status

approved