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A277552
Primes q with prime gap q - p of n-th record merit.
2
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
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
Sequence in context: A062530 A089628 A083841 * A154941 A062601 A231017
KEYWORD
nonn
AUTHOR
Bobby Jacobs, Nov 07 2016
EXTENSIONS
More terms from Robert G. Wilson v, Nov 07 2016
STATUS
approved