A201252 Initial primes in prime septuplets (p, p+2, p+8, p+12, p+14, p+18, p+20) preceding the maximal gaps in A201251.

5639, 88799, 284729, 1146779, 8573429, 24001709, 43534019, 87988709, 157131419, 522911099, 706620359, 1590008669, 2346221399, 3357195209, 11768282159, 30717348029, 33788417009, 62923039169, 68673910169, 88850237459, 163288980299, 196782371699, 421204876439

Offset: 1

Author

Alexei Kourbatov, Nov 28 2011

Keywords

• nonn
• hard

Comments

Prime septuplets (p, p+2, p+8, p+12, p+14, p+18, p+20) are one of the two types of densest permissible constellations of 7 primes. Maximal gaps between septuplets of this type are listed in A201251; see more comments there. A233038 lists the corresponding primes at the end of the maximal gaps.

Examples

			The gap of 83160 between septuplets starting at p=5639 and p=88799 is the very first gap, so a(1)=5639. The gap of 195930 between septuplets starting at p=88799 and p=284729 is a maximal gap - larger than any preceding gap; therefore a(2)=88799. The next gap starts at p=284729 and is again a maximal gap, so a(3)=284729. The next gap is smaller, so it does not contribute to the sequence.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..52
• Tony Forbes, Prime k-tuplets
• Alexei Kourbatov, Maximal gaps between prime k-tuples
• Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053, 2013.
• Eric W. Weisstein, k-Tuple Conjecture

Crossrefs

Cf. A022010 (prime septuplets p, p+2, p+8, p+12, p+14, p+18, p+20), A201251, A233038.