A335045 Minimal common prime of two Goldbach partitions of 2n and 2(n+1) or zero if no common prime exists.

0, 3, 3, 5, 7, 3, 5, 7, 3, 5, 7, 23, 11, 13, 3, 5, 7, 0, 11, 13, 3, 5, 7, 47, 11, 13, 53, 17, 19, 3, 5, 7, 0, 11, 13, 3, 5, 7, 0, 11, 13, 83, 17, 19, 89, 23, 37, 0, 29, 31, 3, 5, 7, 3, 5, 7, 113, 11, 13, 0, 17, 19, 0, 23, 31, 131, 29, 31, 3, 5, 7, 0, 11, 13, 3, 5, 7, 0, 11, 13, 0, 17, 19, 167, 23, 37, 173

Offset

2,2

Comments

a(n) is the least prime p such that 2n-p is in A001359, or 0 if no such p exists. - Robert Israel, May 21 2020

Links

Table of n, a(n) for n=2..88.

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 = 3+13, so a(14/2) = a(7) = 3.

Maple

N:= 100:
P:= select(isprime, {seq(i, i=3..2*N-1, 2)}):
T:= P intersect map(`-`, P, 2):
f:= n -> subs(infinity=0, min(P intersect map(t -> 2*n-t, T))):
map(f, [$2..N]); # Robert Israel, May 21 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, Min[e[n]]]; f/@Range[2, 100]

Crossrefs

Cf. A001359, A002372, A002373, A002375, A045917, A335046.

Sequence in context: A164914 A247479 A134855 * A110246 A070543 A342194

Adjacent sequences: A335042 A335043 A335044 * A335046 A335047 A335048

Keyword

nonn

Author

Ivan N. Ianakiev, May 21 2020

Status

approved