A257313 a(1) = 10; a(2) = 11; for n > 2, a(n) is the smallest number of the form prime + 8 not already used which shares a factor with a(n-1).

10, 11, 55, 15, 21, 27, 39, 13, 91, 49, 105, 25, 45, 51, 69, 75, 81, 87, 111, 37, 259, 147, 117, 135, 115, 145, 165, 121, 187, 231, 159, 171, 19, 247, 285, 175, 189, 201, 67, 469, 301, 315, 205, 235, 265, 325, 345, 207, 219, 237, 79, 1027, 429, 249, 279, 31

Offset: 1

Author

Vladimir Shevelev, Apr 20 2015

Keywords

• nonn

Comments

Analog of EKG-sequence (A064413) on the numbers of the form prime + 8.

Conjecture: the sequence {a(n)-8} is a permutation of primes (A000040).

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A064413, A257311, A257312, A257314, A257315.

Programs

Mathematica

f[n_] := Block[{o = 2^3, s, p, k}, s = {o + 2, o + 3}; For[k = 3, k <= n, k++, p = 2; While[GCD[p + o, s[[k - 1]]] == 1 || MemberQ[s, p + o], p = NextPrime@ p]; AppendTo[s, p + o]]; s]; f@ 56 (* Michael De Vlieger, Apr 20 2015 *)

Extensions

More terms from Peter J. C. Moses, Apr 20 2015