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

Author

Farideh Firoozbakht, Aug 11 2003

Keywords

• nonn

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

Examples

			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.
		

References

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

Crossrefs

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

Programs

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 *)

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

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