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

1,1

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.

Links

Table of n, a(n) for n=1..64.

Formula

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

Example

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..

Mathematica

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

Crossrefs

Cf. A001223, A080374, A080375, A080376.

Sequence in context: A072791 A058320 A014320 * A086526 A086529 A054409

Adjacent sequences: A080374 A080375 A080376 * A080378 A080379 A080380

Keyword

nonn

Author

Labos Elemer, Feb 27 2003

Extensions

More terms from Amiram Eldar, Feb 09 2025

Status

approved