

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
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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 nth and (n+1)th sublists of prime numbers defined in A348178.  YaPing 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}]


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



