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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.
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10, 16, 18, 22, 34, 42, 46, 64, 82, 96, 98, 110, 136, 140, 154, 160, 188, 190, 194, 218, 224, 230, 236, 244, 256, 274, 280, 308, 314, 338, 340, 350, 368, 370, 382, 388, 394, 398, 400, 404, 422, 428, 440, 446, 452, 466, 470, 488, 494, 500, 512, 514, 524, 536, 574, 578, 580, 586
EXAMPLE
82 is in the sequence since it 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.
Primes "p" 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.
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3, 3, 5, 3, 3, 11, 3, 3, 23, 13, 31, 31, 47, 61, 3, 23, 31, 53, 31, 61, 61, 73, 73, 3, 83, 3, 23, 31, 151, 61, 83, 73, 31, 131, 23, 131, 131, 61, 131, 31, 199, 151, 61, 73, 73, 3, 31, 151, 157, 61, 73, 251, 151, 157, 3, 31, 131, 23, 151, 157
EXAMPLE
a(9) = 23; 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 "p" in the definition is 23.
Primes "q" 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.
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7, 13, 13, 19, 31, 31, 43, 61, 59, 83, 67, 79, 89, 79, 151, 137, 157, 137, 163, 157, 163, 157, 163, 241, 173, 271, 257, 277, 163, 277, 257, 277, 337, 239, 359, 257, 263, 337, 269, 373, 223, 277, 379, 373, 379, 463, 439, 337, 337, 439, 439, 263, 373, 379, 571, 547, 449, 563, 439, 439
EXAMPLE
a(9) = 59; 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 "q" in the definition is 59.
Primes "s" 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.
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4
5, 11, 11, 17, 29, 29, 41, 59, 53, 79, 61, 73, 83, 73, 149, 131, 151, 131, 157, 151, 157, 151, 157, 239, 167, 269, 251, 271, 157, 271, 251, 271, 331, 233, 353, 251, 257, 331, 263, 367, 211, 271, 373, 367, 373, 461, 433, 331, 331, 433, 433, 257, 367, 373, 569, 541, 443, 557, 433, 433
EXAMPLE
a(9) = 53; 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 "s" in the definition is 53.
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