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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.

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A337435 6*a(n) - 1 is the least prime p of a pair of twin primes p, p + 2, for which the prime gap immediately below p achieves the size 2*A007494(n).

Original entry on oeis.org

2, 5, 25, 87, 325, 213, 192, 758, 500, 1158, 1668, 5383, 4217, 13130, 15180, 4713, 5955, 19583, 66642, 17127, 48108, 49485, 28905, 171005, 175530, 61838, 314192, 76967, 192637, 96147, 812768, 708780, 139725, 295862, 354545, 1572328, 1240860, 1681368, 773453, 1300602
Offset: 1

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Author

Hugo Pfoertner, Sep 02 2020

Keywords

Comments

Apart from the atypical case [3, 5, 7], prime gaps p - prevprime(p-1) preceding a pair of twin primes p, p+2 can only have the sizes 4, 6, 10, 12, 16, 18, ..., i.e., numbers k of the form 2*(k == 0 or 2 mod 3) = 2*A007494(n).

Examples

			a(1) = 2: The first occurrence of 3 consecutive primes [p-4, p, p+2] is at p = 6*a(1) - 1 = 11 -> [7, 11, 13],
a(2) = 5: consecutive primes [p-6, p, p+2] first occur at p = 6*a(2) - 1 = 29 -> [23, 29, 31],
a(3) = 25: consecutive primes [p-10, p, p+2] first occur at p = 6*a(3) - 1 = 149 -> [139, 149, 151].

Crossrefs

Cf. A007494, A329158, A329159, A337436.
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