OFFSET
1,1
COMMENTS
Analog of EKG-sequence (A064413) on the numbers of the form prime + 2.
Conjecture: the sequence {a(n)-2} is a permutation of the primes (A000040).
Every prime in the sequence is greater of twin primes (A006512).
A generalization. Let A_k (k>=1) be the following sequence: a(1) = 2^k+2; a(2) = 2^k+3; for n > 2, a(n) is the smallest number of the form 2^k+prime not already used which shares a factor with a(n-1).
Conjecture: For every k>=1, the sequence A_k - 2^k is a permutation of the primes.
LINKS
Peter J. C. Moses, Table of n, a(n) for n = 1..1000
MATHEMATICA
f[n_] := Block[{o = 2, 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@ 58 (* Michael De Vlieger, Apr 20 2015 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Apr 20 2015
EXTENSIONS
More terms from Peter J. C. Moses, Apr 20 2015
STATUS
approved