A233434 - OEIS

%I #11 Feb 16 2025 08:33:21

%S 11,41,101,191,461,641,1091,1871,2657,3251,6827,7877,40427,47711,

%T 58907,86111,171047,379007,385391,553097

%N Primes p in prime triples (p, p+2, p+6) at the end of the maximal gaps in A201598.

%C Prime triples (p, p+2, p+6) are one of the two types of densest permissible constellations of 3 primes. Maximal gaps between triples of this type are listed in A201598; see more comments there.

%H Alexei Kourbatov, <a href="/A233434/b233434.txt">Table of n, a(n) for n = 1..72</a>

%H Tony Forbes, <a href="http://anthony.d.forbes.googlepages.com/ktuplets.htm">Prime k-tuplets</a>

%H Alexei Kourbatov, <a href="http://www.javascripter.net/math/primes/maximalgapsbetweenprimetriplets.htm">Maximal gaps between prime triples</a>

%H Alexei Kourbatov, <a href="http://arxiv.org/abs/1309.4053">Tables of record gaps between prime constellations</a>, arXiv preprint arXiv:1309.4053, 2013.

%H Eric W. Weisstein, <a href="https://mathworld.wolfram.com/k-TupleConjecture.html">k-Tuple Conjecture</a>

%e The gap of 6 between triples starting at p=5 and p=11 is the very first gap, so a(1)=11. The gap of 6 between triples starting at p=11 and p=17 is not a record, so a new term is not added. The gap of 24 between triples starting at p=17 and p=41 is a record gap - larger than any preceding gap; therefore a(2)=41.

%Y Cf. A022004, A201598, A201599.

%K nonn,changed

%O 1,1

%A _Alexei Kourbatov_, Dec 09 2013