A133234 a(n) is least semiprime (not already in list) such that no 3-term subset forms an arithmetic progression.

4, 6, 9, 10, 15, 22, 25, 33, 39, 49, 55, 58, 82, 86, 87, 93, 111, 118, 121, 122, 134, 145, 185, 194, 201, 202, 206, 215, 237, 247, 274, 287, 298, 299, 303, 305, 314, 334, 335, 358, 362, 386, 446, 447, 454, 471, 482, 497, 502, 527, 529, 537, 553, 554, 562, 614

Offset

1,1

Comments

This is to semiprimes A001358 as A131741 is to primes A000040.

Links

Table of n, a(n) for n=1..56.

Formula

a(1) = 4, a(2) = 6, a(n) = smallest semiprime such that there is no i < j < n with a(n) - a(j) = a(j) - a(i).

Mathematica

NextSemiprime[n_] := Block[{c = n + 1, f = 0}, While[Plus @@ Last /@ FactorInteger[c] != 2, c++ ]; c ]; f[l_List] := Block[{c, f = 0}, c = If[l == {}, 2, l[[ -1]]]; While[f == 0, c = NextSemiprime[c]; If[Intersection[l, l - (c - l)] == {}, f = 1]; ]; Append[l, c] ]; Nest[f, {}, 100] (* Ray Chandler, Nov 10 2007 *)

Crossrefs

Cf. A000040, A001358, A065825, A131741.

Sequence in context: A119961 A122492 A178378 * A111206 A087112 A077554

Adjacent sequences: A133231 A133232 A133233 * A133235 A133236 A133237

Keyword

easy,nonn

Author

Jonathan Vos Post, Oct 13 2007

Extensions

More terms from Ray Chandler, Nov 10 2007

Status

approved