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A352445
Smallest prime "p" 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.
4
3, 3, 5, 3, 5, 7, 3, 5, 11, 3, 5, 7, 13, 3, 5, 11, 3, 5, 23, 11, 7, 13, 31, 19, 3, 5, 31, 3, 5, 7, 13, 19, 47, 7, 61, 3, 5, 11, 3, 5, 23, 11, 17, 7, 13, 3, 5, 31, 53, 11, 31, 3, 5, 3, 5, 11, 17, 61, 47, 29, 61, 47, 29, 73, 3, 5, 73, 7, 3, 5, 11, 83, 17, 23, 37, 29, 3, 5, 23
OFFSET
1,1
FORMULA
a(n) = A352240(n) - A352444(n).
EXAMPLE
a(12) = 7; 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 smallest prime "p" among all Goldbach pairs is 7.
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Mar 16 2022
STATUS
approved