A277552 Primes q with prime gap q - p of n-th record merit.

3, 5, 11, 127, 1151, 1361, 19661, 31469, 156007, 360749, 370373, 1357333, 2010881, 17051887, 20831533, 191913031, 436273291, 2300942869, 3842611109, 4302407713, 10726905041, 25056082543, 304599509051, 461690510543, 1346294311331, 1408695494197, 1968188557063, 2614941711251, 13829048560417, 19581334193189

Offset

1,1

Comments

The merit of the gap between consecutive primes p and q is (q-p)/log(p).

This sequence is infinite (Westzynthius 1931). - Charles R Greathouse IV, Nov 10 2016

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = A111870(n) + A111871(n). - Charles R Greathouse IV, Nov 11 2016

Mathematica

p = 2; q = 3; lmt = 0; lst = {}; While[p < 10^12, If[q > p + lmt*Log[p], AppendTo[lst, q]; Print[q]; lmt = (q - p)/Log[p]]; p = q; q = NextPrime@ p]; lst (* or *)
(* set lst = the terms in A111870 *) NextPrime[ lst] (* Robert G. Wilson v, Nov 07 2016 *)

Prog

(PARI) r=rm=0; p=2; forprime(q=3, , t=q-p; if(t>r, r=t; t/=log(p); if(t>rm, rm=t; print1(q", "))); p=q) \\ Charles R Greathouse IV, Nov 11 2016

Crossrefs

Cf. A111870, A111871.

Sequence in context: A062530 A089628 A083841 * A154941 A062601 A231017

Adjacent sequences: A277549 A277550 A277551 * A277553 A277554 A277555

Keyword

nonn

Author

Bobby Jacobs, Nov 07 2016

Extensions

More terms from Robert G. Wilson v, Nov 07 2016

Status

approved