A352353 - OEIS

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A352353

Primes "r" corresponding to the even numbers with exactly 1 pair of Goldbach partitions, (p,q) and (r,s) with p,q,r,s prime and p < r <= s < q, such that all integers in the open intervals (p,r) and (s,q) are composite.

5, 5, 7, 5, 5, 13, 5, 5, 29, 17, 37, 37, 53, 67, 5, 29, 37, 59, 37, 67, 67, 79, 79, 5, 89, 5, 29, 37, 157, 67, 89, 79, 37, 137, 29, 137, 137, 67, 137, 37, 211, 157, 67, 79, 79, 5, 37, 157, 163, 67, 79, 257, 157, 163, 5, 37, 137, 29, 157, 163

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OFFSET

1,1

COMMENTS

See A352297.

LINKS

Table of n, a(n) for n=1..60.

Eric Weisstein's World of Mathematics, Goldbach Partition

Wikipedia, Goldbach's conjecture

Index entries for sequences related to Goldbach conjecture

Index entries for sequences related to partitions

FORMULA

a(n) = A352297(n) - A352354(n).

EXAMPLE

a(9) = 29; A352297(9) = 82 has exactly one pair of Goldbach partitions, namely (23,59) and (29,53), such that all integers in the open intervals (23,29) and (53,59) are composite. The prime corresponding to "r" in the definition is 29.

CROSSREFS

Cf. A352297, A352248, A352283, A352240.

Cf. A352351 (for primes "p"), A352352 (for primes "q"), A352354 (for primes "s").

Sequence in context: A122273 A052247 A088201 * A195380 A139261 A352442

Adjacent sequences: A352350 A352351 A352352 * A352354 A352355 A352356

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Mar 12 2022

STATUS

approved