cp's OEIS Frontend

A378429 Numbers k such that the prime gap between the consecutive primes p1 < k# = primorial(k) < p2 sets a new record.

%I A378429 #44 Dec 23 2024 04:39:49
%S A378429 3,7,13,17,23,29,37,43,47,61,71,79,83,97,101,109,137,193,347,349,409,
%T A378429 457,587,599,887,929,967,1319,1801,1877,2081,2687,2731,2741,2843,2939,
%U A378429 2957,3673,3823,4621,5717,6011,6151,6563,6863,7393,8389,9833,11903,12547
%N A378429 Numbers k such that the prime gap between the consecutive primes p1 < k# = primorial(k) < p2 sets a new record.
%e A378429 a(1) = 3, because the prime gap between the consecutive primes 5 < 3# < 7 sets the first record of 2.
%e A378429  n gap       p1        a(n)#        p2
%e A378429  1   2             5 <   3# <             7
%e A378429  2  12           199 <   7# <           211
%e A378429  3  18         30029 <  13# <         30047
%e A378429  4  48        510481 <  17# <        510529
%e A378429  5  80     223092827 <  23# <     223092907
%e A378429  6 102    6469693189 <  29# <    6469693291
%e A378429  7 120 7420738134751 <  37# < 7420738134871
%Y A378429 Cf. A001223, A058044, A034386, A350100.
%K A378429 nonn
%O A378429 1,1
%A A378429 _Jean-Marc Rebert_, Dec 20 2024
%E A378429 a(32)-a(39) from _Amiram Eldar_, Dec 20 2024
%E A378429 a(40)-a(50) from _Michael S. Branicky_, Dec 21 2024