A085237 Nondecreasing gaps between primes.

1, 2, 2, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 8, 14, 14, 14, 18, 20, 22, 34, 34, 36, 36, 36, 44, 52, 52, 72, 86, 86, 96, 112, 114, 118, 132, 132, 148, 154, 154, 154, 180, 210, 220, 222, 234, 248, 250, 250, 282, 288, 292, 320, 336, 336, 354, 382, 384, 394, 456, 464, 468, 474, 486, 490, 500, 514, 516, 532, 534, 540, 582, 588, 602, 652, 674, 716, 766, 778

Offset

1,2

Comments

All terms of A005250 are in the sequence, but some terms of A005250 appear in this sequence more than once.

a(n) is the gap between the n-th and (n+1)-th sublists of prime numbers defined in A348178. - Ya-Ping Lu, Oct 19 2021

References

R. K. Guy, Unsolved problems in number theory.

Links

Table of n, a(n) for n=1..79.

Example

a(21) = a(22) = 34 because prime(218) - prime(217) = prime(1060) - prime(1059) = 34 and prime(n+1) - prime(n) is less than 34, for n < 1059 and n not equal to 217.

Mathematica

f[n_] := Prime[n+1]-Prime[n]; v={}; Do[ If[f[n]>=If[n==1, 1, v[[ -1]]], v1=n; v=Append[v, f[v1]]; Print[v]], {n, 105000000}]
DeleteDuplicates[Differences[Prime[Range[10^7]]], Greater] (* Harvey P. Dale, Jan 17 2024 *)

Prog

(Python)
from sympy import nextprime; p, r = 2, 0
while r < 778:
    q = nextprime(p); g = q - p
    if g >= r: print(g, end = ', '); r = g
    p = q # Ya-Ping Lu, Jan 23 2024

Crossrefs

Cf. A005250, A005669, A053686, A002386, A348178.

Sequence in context: A292264 A265263 A113320 * A279891 A110870 A206224

Adjacent sequences: A085234 A085235 A085236 * A085238 A085239 A085240

Keyword

nonn

Author

Farideh Firoozbakht, Aug 11 2003

Extensions

a(53)-a(63) from Donovan Johnson, Nov 24 2008

a(64)-a(76) from Charles R Greathouse IV, May 09 2011

a(77)-a(79) from Charles R Greathouse IV, May 19 2011

Status

approved