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

1,1

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.

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

Example

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.

Crossrefs

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

Sequence in context: A116622 A013794 A022009 * A144837 A324267 A085017

Adjacent sequences: A201246 A201247 A201248 * A201250 A201251 A201252

Keyword

nonn,hard

Author

Alexei Kourbatov, Nov 28 2011

Status

approved