A352442 - OEIS

A352442

Largest prime "r" among all pairs of Goldbach partitions of A352240(n), (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, 11, 13, 5, 17, 13, 5, 19, 17, 29, 5, 23, 31, 29, 19, 29, 41, 37, 17, 37, 43, 53, 41, 37, 29, 53, 59, 53, 61, 53, 41, 67, 59, 47, 71, 5, 47, 29, 79, 71, 73, 83, 53, 83, 37, 59, 83, 37, 29, 71, 29, 101, 103, 107, 67, 89, 73, 67, 59, 101, 79, 59, 107, 79, 113, 5, 109

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OFFSET

1,1

COMMENTS

See A352240.

LINKS

Table of n, a(n) for n=1..70.

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) = A352240(n) - A352443(n).

EXAMPLE

a(12) = 17; A352240(12) = 54 has 3 pairs of Goldbach partitions (7,47),(11,43); (11,43),(13,41); and (13,41),(17,37); with all integers composite in the open intervals (7,11) and (43,47), (11,13) and (41,43), and, (13,17) and (37,41) respectively. The largest prime "r" among the Goldbach pairs is 17.

CROSSREFS

Cf. A187797, A278700, A352240, A352248, A352283.

Cf. A352443, A352444, A352445.

Sequence in context: A352353 A195380 A139261 * A247649 A252655 A021646

Adjacent sequences: A352439 A352440 A352441 * A352443 A352444 A352445

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Mar 16 2022

STATUS

approved