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A277552 Primes q with prime gap q - p of n-th record merit. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified March 28 15:06 EDT 2020. Contains 333089 sequences. (Running on oeis4.)