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

Author

Hugo Pfoertner, Sep 03 2021

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Subset of A001359.

Cf. A262935, A262936.