A347280 Let P1>3, P2, P3, P4 be 4 consecutive primes with P3-P2 = 2. a(n) = P2 is the earliest occurrence of the 4-tuple with min(P2-P1, P4-P3) = 2*n, or 0 if no such constellation exists.

11, 29, 0, 419, 521, 0, 1931, 6449, 0, 10037, 43541, 0, 10007, 28349, 0, 107507, 280409, 0, 261167, 173429, 0, 569321, 913637, 0, 1598447, 1789091, 0, 1349531, 5317451, 0, 17282051, 25844561, 0, 10851161, 28582787, 0, 36126917, 14318657, 0, 60117947, 42062717

Offset

2,1

Comments

The "irregular" constellation 3, 5, 7, 11 is intentionally excluded.

Links

Hugo Pfoertner, Table of n, a(n) for n = 2..113

Example

a(2) = 11, because min(11-7, 17-13) = 4 is the earliest occurrence of the minimum gap of 2*2 = 4 adjacent to a pair of twin primes.
a(3) = 29: the constellation 23, 29, 31, 37 has min(29-23, 37-31) = 2*3 = 6, whereas the preceding constellations 7, 11, 13, 19, and 13, 17, 19, 23 don't yield a minimum of 6.
a(5) = 419: 409, 419, 421, 431 leads to the earliest occurrence of the minimum adjacent gap of 2*5.

Crossrefs

Subset of A001359.

Cf. A262935, A262936.

Sequence in context: A018944 A061086 A201633 * A274130 A034276 A245169

Adjacent sequences: A347277 A347278 A347279 * A347281 A347282 A347283

Keyword

nonn

Author

Hugo Pfoertner, Sep 03 2021

Status

approved