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 A335046 Maximal common prime of two Goldbach partitions of 2n and 2(n+1) or zero (if common prime does not exist). 1
 0, 3, 5, 7, 7, 11, 13, 13, 17, 19, 19, 23, 23, 19, 29, 31, 31, 0, 37, 37, 41, 43, 43, 47, 47, 43, 53, 53, 43, 59, 61, 61, 0, 67, 67, 71, 73, 73, 0, 79, 79, 83, 83, 79, 89, 89, 79, 0, 97, 97, 101, 103, 103, 107, 109, 109, 113, 113, 109, 0, 113, 109, 0, 127, 127, 131, 131, 127, 137, 139, 139 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 LINKS EXAMPLE 4 = 2+2 and 6 = 3+3. Since those are the only available Goldbach partitions and they have no common prime, a(4/2) = a(2) = 0. 14 = 3+11 and 16 = 5+11, so a(14/2) = a(7) = 11. MAPLE S:= proc(n) option remember; {seq((h-> `if`(       andmap(isprime, h), h, [])[])([n+i, n-i]), i=0..n-2)}     end: a:= n-> max(0, (S(n) intersect S(n+1))[]): seq(a(n), n=2..80);  # Alois P. Heinz, Jun 20 2020 MATHEMATICA d[n_]:=Flatten[Cases[FrobeniusSolve[{1, 1}, 2*n], {__?PrimeQ}]] e[n_]:=Intersection[d[n], d[n+1]]; f[n_]:=If[e[n]=={}, 0, Max[e[n]]]; f/@Range[2, 100] CROSSREFS Cf. A002372, A002373, A002375, A045917, A060308, A335045. Sequence in context: A260940 A037464 A302564 * A060265 A172365 A297709 Adjacent sequences:  A335043 A335044 A335045 * A335047 A335048 A335049 KEYWORD nonn AUTHOR Ivan N. Ianakiev, May 21 2020 STATUS approved

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Last modified December 5 12:24 EST 2021. Contains 349557 sequences. (Running on oeis4.)