A329161 - OEIS

%I #9 Mar 02 2020 00:51:21

%S 2,3,5,6,9,12,14,15,17,21,26,27,29,30,35,41,45,50,59,60,63,71,74,75,

%T 84,92,96,98,104,110,125,129,144,155,156,165,180,201,204,207

%N 2*a(n) are the lengths of record prime gaps immediately following twin primes.

%C The corresponding locations are provided in A329160, starting at the initial pair 5, 7.

%e a(1) = 2 because the prime gap after 5, 7 has length 11 - 7 = 2*a(1) = 4,

%e a(2) = 3 because the prime gap after 29,31 has length 37 - 31 = 2*a(2) = 6, with location given by 6*A329160(2) = 30 +- 1. The gaps before all have length 4 (11,13 -> 17), (17,19 -> 23).

%o (PARI) p1=5; p2=7; r=0; forprime(p3=11, 1e9, if(p2-p1==2, d=p3-p2; if(d>r, r=d; print1(d/2, ", "))); p1=p2; p2=p3)

%Y Cf. A329158, A329159, A329160, A329164, A329165.

%K nonn,more

%O 1,1

%A _Hugo Pfoertner_, Nov 08 2019

%E a(39)-a(40) from _Jinyuan Wang_, Mar 01 2020