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A352240
Even numbers with at least one 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.
11
10, 16, 18, 22, 24, 30, 34, 36, 42, 46, 48, 54, 60, 64, 66, 72, 76, 78, 82, 84, 90, 96, 98, 102, 106, 108, 110, 112, 114, 120, 126, 132, 136, 138, 140, 142, 144, 150, 154, 156, 160, 162, 168, 174, 180, 184, 186, 188, 190, 192, 194, 196, 198, 202, 204, 210, 216, 218, 220, 222
OFFSET
1,1
COMMENTS
Similar to A187797 but also contains the numbers 82, 96, 98, 110, 136, ...
FORMULA
a(n) = A352442(n) + A352443(n).
a(n) = A352444(n) + A352445(n).
EXAMPLE
82 is in the sequence since it has at least 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.
MATHEMATICA
Table[If[Sum[Sum[KroneckerDelta[NextPrime[k], i]*KroneckerDelta[NextPrime[2 n - i], 2 n - k]*(PrimePi[k] - PrimePi[k - 1]) (PrimePi[2 n - k] - PrimePi[2 n - k - 1]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[2 n - i] - PrimePi[2 n - i - 1]), {k, i}], {i, n}] > 0, 2 n, {}], {n, 150}] // Flatten
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Mar 08 2022
STATUS
approved