A080377 Prime gaps where A080374 increases.

2, 4, 6, 8, 14, 10, 18, 22, 34, 16, 26, 32, 38, 50, 62, 54, 58, 46, 64, 86, 82, 74, 98, 106, 94, 118, 122, 128, 146, 134, 142, 162, 178, 158, 166, 202, 194, 206, 214, 218, 242, 250, 226, 254, 274, 262, 256, 278, 326, 302, 298, 314, 382, 346, 358, 338, 394, 334, 386, 362, 398, 446, 454, 486

Offset: 1

Author

Labos Elemer, Feb 27 2003

Keywords

• nonn

Comments

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.

Examples

			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.
22 is the 8th term: in the first 7 terms 11 is not a prime factor unlike 22.
Several even numbers do not arise in this sequence, e.g., 12, 20, 36, 48, etc..
		

Crossrefs

Cf. A001223, A080374, A080375, A080376.

Programs

Mathematica

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

Formula

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

Extensions

More terms from Amiram Eldar, Feb 09 2025