cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A352297 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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Wesley Ivan Hurt, Mar 11 2022

Keywords

Examples

			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.

Links

Crossrefs

Cf. A187797, A278700, A352248, A352283, A352240.
Cf. See A352351, A352352, A352353, and A352354 for values of the corresponding primes p, q, r, and s.

Formula

a(n) = A352351(n) + A352352(n) = A352353(n) + A352354(n).

A352352 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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Wesley Ivan Hurt, Mar 12 2022

Keywords

Comments

See A352297.

Examples

			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.

Links

Crossrefs

Cf. A352297, A352248, A352283, A352240.
Cf. A352351 (for primes "p"), A352353 (for primes "r"), A352354 (for primes "s").

Formula

a(n) = A352297(n) - A352351(n).

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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Wesley Ivan Hurt, Mar 12 2022

Keywords

Comments

See A352297.

Examples

			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.

Links

Crossrefs

Cf. A352297, A352248, A352283, A352240.
Cf. A352351 (for primes "p"), A352352 (for primes "q"), A352354 (for primes "s").

Formula

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

A352354 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.

Original entry on oeis.org

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
Offset: 1

Views

Author

Wesley Ivan Hurt, Mar 12 2022

Keywords

Comments

See A352297.

Examples

			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.

Links

Crossrefs

Cf. A352297, A352248, A352283, A352240.
Cf. A352351 (for primes "p"), A352352 (for primes "q"), A352353 (for primes "r").

Formula

a(n) = A352297(n) - A352353(n).
Showing 1-4 of 4 results.

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