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A085237
Nondecreasing gaps between primes.
5
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.
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
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