cp's OEIS Frontend

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.

%I A065978 #62 Aug 01 2021 01:54:02
%S A065978 4,8,16,44,92,242,256,272,292,476,530,572,682,688,1052,1808,2228,3382,
%T A065978 3472,3502,3562,4952,6194,7102,10262,17008,20684,37052,45128,49552,
%U A065978 80144,137414,251806,349826,362534,742856,1655152,1872236,2108282,2319728,2707118
%N 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.
%C A065978 The values of f(a(n)) (given in A066286) appear to be divisible by 6, except the first two.
%H A065978 Gilmar Rodriguez Pierluissi, <a href="/A065978/b065978.txt">Table of n, a(n) for n = 1..64</a> (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)
%e A065978 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.
%e A065978 10=5+5 (0), 12=5+7 (2), 14=7+7 (0), 16=5+11 (6), so 16 is in the sequence.
%t A065978 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]]]
%Y A065978 Cf. A066285, A066286, A107926.
%K A065978 nonn,nice
%O A065978 1,1
%A A065978 _Jon Perry_, Dec 09 2001
%E A065978 More terms from _Robert G. Wilson v_ and _Dean Hickerson_, Dec 10 2001
%E A065978 Changed offset to 1 (this is a list). - _N. J. A. Sloane_, Sep 07 2013