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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 (list; graph; refs; listen; history; text; internal format)
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[n-p], Return[n-2p]]]; 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

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Last modified October 26 14:28 EDT 2021. Contains 348267 sequences. (Running on oeis4.)