A201249 Initial primes in prime septuplets (p, p+2, p+6, p+8, p+12, p+18, p+20) preceding the maximal gaps in A201051.

11, 165701, 1068701, 25658441, 45002591, 93625991, 257016491, 367438061, 575226131, 1228244651, 1459270271, 2923666841, 10180589591, 15821203241, 23393094071, 37846533071, 158303571521, 350060308511, 382631592641, 711854781551, 2879574595811, 3379186846151

Offset: 1

Author

Alexei Kourbatov, Nov 28 2011

Keywords

• nonn
• hard

Comments

Prime septuplets (p, p+2, p+6, p+8, p+12, 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 A201051; see more comments there.

Examples

			The gap of 165690 between septuplets starting at p=11 and p=165701 is the very first gap, so a(1)=11. The gap of 903000 between septuplets starting at p=165701 and p=1068701 is a maximal gap - larger than any preceding gap; therefore a(2)=165701. The next gap of 10831800 starts at p=1068701 and is again a maximal gap, so a(3)=1068701. The next gap is smaller, so it does not contribute to the sequence.
		

Links

• Alexei Kourbatov, Table of n, a(n) for n = 1..36
• Tony Forbes, Prime k-tuplets
• Alexei Kourbatov, Maximal gaps between prime septuplets
• Alexei Kourbatov, Tables of record gaps between prime constellations, arXiv preprint arXiv:1309.4053, 2013.
• Eric W. Weisstein, k-Tuple Conjecture

Crossrefs

Cf. A022009 (prime septuplets p, p+2, p+6, p+8, p+12, p+18, p+20), A201051, A233425.