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A257311
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a(1) = 4; a(2) = 5; for n > 2, a(n) is the smallest number of the form prime + 2 not already used which shares a factor with a(n-1).
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6
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4, 5, 15, 9, 21, 7, 49, 63, 33, 39, 13, 91, 105, 25, 45, 55, 75, 69, 81, 99, 111, 129, 43, 559, 169, 195, 85, 115, 165, 141, 153, 159, 183, 61, 549, 201, 213, 225, 175, 133, 19, 285, 231, 243, 273, 259, 315, 235, 265, 295, 355, 375, 279, 31, 403, 351, 309, 103
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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