

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
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OFFSET

2,2


LINKS

Table of n, a(n) for n=2..72.
Index entries for sequences related to Goldbach conjecture


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, ni]), i=0..n2)}
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



