

A065978


For even k >= 4, let f(k) = A066285(k/2) be the minimal difference between primes p and q whose sum is k. Such a k is in the sequence if f(k) > f(m) for all even m with 4 <= m < k.


7



4, 8, 16, 44, 92, 242, 256, 272, 292, 476, 530, 572, 682, 688, 1052, 1808, 2228, 3382, 3472, 3502, 3562, 4952, 6194, 7102, 10262, 17008, 20684, 37052, 45128, 49552, 80144, 137414, 251806, 349826, 362534, 742856, 1655152, 1872236, 2108282, 2319728, 2707118
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OFFSET

1,1


COMMENTS

The values of f(a(n)) (given in A066286) appear to be divisible by 6, except the first two.


LINKS

Gilmar Rodriguez Pierluissi, Table of n, a(n) for n = 1..64 (terms 1..50 from Jon Perry, Robert G. Wilson and Dean Hickerson, terms 51..55 from Gilmar Rodriguez Pierluissi, terms 56..63 from Robert G. Wilson v)


EXAMPLE

4 = 2+2; the gap is 0. 6=3+3 (0). 8=3+5; the gap is 2, and this is the largest gap to date, so 8 is in the sequence.
10=5+5 (0), 12=5+7 (2), 14=7+7 (0), 16=5+11 (6), so 16 is in the sequence.


MATHEMATICA

f[n_] := For[p=n/2, True, p, If[PrimeQ[p]&&PrimeQ[np], Return[n2p]]]; For[n=4; max=1, True, n+=2, If[f[n]>max, Print[n]; max=f[n]]]


CROSSREFS

Cf. A066285, A066286, A107926.
Sequence in context: A144687 A278377 A065605 * A077447 A337783 A301773
Adjacent sequences: A065975 A065976 A065977 * A065979 A065980 A065981


KEYWORD

nonn,nice


AUTHOR

Jon Perry, Dec 09 2001


EXTENSIONS

More terms from Robert G. Wilson v and Dean Hickerson, Dec 10 2001
Changed offset to 1 (this is a list).  N. J. A. Sloane, Sep 07 2013


STATUS

approved



