A125505 Number of arithmetic progressions of primes (p,q,r) of length 3 with r <= prime(n).

0, 0, 0, 1, 2, 2, 3, 5, 7, 9, 11, 11, 13, 16, 17, 20, 23, 24, 26, 30, 32, 36, 40, 44, 46, 49, 53, 56, 59, 64, 69, 74, 78, 83, 87, 92, 95, 100, 105, 111, 115, 119, 126, 129, 135, 142, 148, 155, 160, 164, 169, 173, 179, 187, 194, 201, 208, 215, 218, 226, 235, 243, 248, 257

Offset

1,5

Links

Table of n, a(n) for n=1..64.

Example

a(4)=1 counts the progression (3,5,7) with all 3 members less than or equal to prime(4)=7.
a(5)=2 counts (3,5,7) and (3,7,11). a(7)=3 counts (3,5,7), (3,7,11) and (5,11,17).
Progressions with length larger than 3 are defined to contribute with each of their sublists: The progression (5,11,17,23) counts twice in a(9), as (5,11,17) and as (11,17,23).

Maple

A125505 := proc(n, verb) local r, p, a, q, strid; a := 0 ; p := 2 ; while p+4 <= ithprime(n) do for strid from 2 do q := p+strid ; r := q+strid ; if r > ithprime(n) then break ; fi ; if isprime(q) and isprime(r) then if verb then print(n, p, q, r) ; fi ; a := a+1 ; fi ; od: p := nextprime(p) ; od: RETURN(a) ; end: seq(A125505(n, false), n=1..80) ; # R. J. Mathar, Nov 21 2007

Crossrefs

Sequence in context: A133393 A126881 A290273 * A357381 A061565 A077075

Adjacent sequences: A125502 A125503 A125504 * A125506 A125507 A125508

Keyword

nonn

Author

Giovanni Teofilatto, Jan 03 2007; definition corrected Jan 26 2007

Extensions

Corrected and extended by R. J. Mathar, Nov 21 2007

Status

approved