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A085237 Nondecreasing gaps between primes.

%I A085237 #35 Feb 15 2024 06:18:19
%S A085237 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,
%T A085237 52,72,86,86,96,112,114,118,132,132,148,154,154,154,180,210,220,222,
%U A085237 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
%N A085237 Nondecreasing gaps between primes.
%C A085237 All terms of A005250 are in the sequence, but some terms of A005250 appear in this sequence more than once.
%C A085237 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
%D A085237 R. K. Guy, Unsolved problems in number theory.
%e A085237 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.
%t A085237 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}]
%t A085237 DeleteDuplicates[Differences[Prime[Range[10^7]]],Greater] (* _Harvey P. Dale_, Jan 17 2024 *)
%o A085237 (Python)
%o A085237 from sympy import nextprime; p, r = 2, 0
%o A085237 while r < 778:
%o A085237     q = nextprime(p); g = q - p
%o A085237     if g >= r: print(g, end = ', '); r = g
%o A085237     p = q # _Ya-Ping Lu_, Jan 23 2024
%Y A085237 Cf. A005250, A005669, A053686, A002386, A348178.
%K A085237 nonn
%O A085237 1,2
%A A085237 _Farideh Firoozbakht_, Aug 11 2003
%E A085237 a(53)-a(63) from _Donovan Johnson_, Nov 24 2008
%E A085237 a(64)-a(76) from _Charles R Greathouse IV_, May 09 2011
%E A085237 a(77)-a(79) from _Charles R Greathouse IV_, May 19 2011