A080377 - OEIS

%I #13 Feb 09 2025 02:48:29

%S 2,4,6,8,14,10,18,22,34,16,26,32,38,50,62,54,58,46,64,86,82,74,98,106,

%T 94,118,122,128,146,134,142,162,178,158,166,202,194,206,214,218,242,

%U 250,226,254,274,262,256,278,326,302,298,314,382,346,358,338,394,334,386,362,398,446,454,486

%N Prime gaps where A080374 increases.

%C a(n+1) is the smallest prime gap (A001223) that has a prime factor not present in previous gaps or was present but at a lower power.

%F a(n) = prime(1+A080376(n)) - prime(A080376(n)).

%e 18 is the 7th term: in the first 6 terms, {2, 4, 6, 8, 14, 10}, 3 does not occur with power 2 unlike in 18 = 2 * 3^2.

%e 22 is the 8th term: in the first 7 terms 11 is not a prime factor unlike 22.

%e Several even numbers do not arise in this sequence, e.g., 12, 20, 36, 48, etc..

%t s=1; Do[s1=s; s=LCM[s, d=Prime[n+1]-Prime[n]]; If[Greater[s, s1], Print[d]], {n, 1, 10000000}]

%Y Cf. A001223, A080374, A080375, A080376.

%K nonn

%O 1,1

%A _Labos Elemer_, Feb 27 2003

%E More terms from _Amiram Eldar_, Feb 09 2025