A122669 Number of nontrivial arithmetic progressions of primes between n and 2n.

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

Offset

1,27

Comments

Count of subsets of at least 3 primes in range that are arithmetic progressions.

Links

Jean-François Alcover, Table of n, a(n) for n = 1..135

Example

a(15)=1 because primes between 15 and 30 are {17, 19, 23, 29} and {17, 23, 29} is an arithmetic progression.
a(27)=a(28)=a(29)=3 because {29, 31, 37, 41, 43, 47, 53} includes {29, 41, 53}, {31, 37, 43}, {41, 47, 53}.
a(30)=4 because {31, 37, 41, 43, 47, 53, 59} includes {31, 37, 43}, {41, 47, 53}, {47, 53, 59}, {41, 47, 53,
59}.

Mathematica

a[n_] := a[n] = Module[{pp, S}, pp = Select[Range[n, 2 n], PrimeQ]; S = Subsets[pp, {3, Length[pp]}]; Select[S, 1 == Length[Union[Differences[#] ]]&] // Length];
Reap[For[n = 1, n <= 135, n++, Print[n, " ", a[n]]; Sow[a[n]]]][[2, 1]] (* Jean-François Alcover, Sep 29 2020 *)

Crossrefs

Sequence in context: A165605 A230194 A128112 * A071942 A289189 A134849

Adjacent sequences: A122666 A122667 A122668 * A122670 A122671 A122672

Keyword

nonn

Author

Giovanni Teofilatto, Sep 24 2006

Extensions

Edited and extended by Ray Chandler, Sep 26 2006

Status

approved