

A122669


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


1



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
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OFFSET

1,27


COMMENTS

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


LINKS

JeanFrançois 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]] (* JeanFrançois 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



