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A246777 a(n) = A246776(A005669(n)): using the indices of maximal primes in A002386 in order to verify the Firoozbakht conjecture for 0 <= floor(prime(n)^(1+1/n)) - prime(n+1).

%I A246777 #30 Jan 28 2022 01:34:05
%S A246777 1,0,0,3,10,5,16,19,20,10,38,38,35,24,43,53,38,43,66,52,46,65,79,55,
%T A246777 73,104,109,95,120,92,130,130,121,127,114,127,155,148,92,109,159,171,
%U A246777 173,180,171,157,171,161,174,178,168,165,169,135,171,168,138,174,195,234,149,253,269,61,244,248,255,323,304,307,262,245,234,215,228
%N A246777 a(n) = A246776(A005669(n)): using the indices of maximal primes in A002386 in order to verify the Firoozbakht conjecture for 0 <= floor(prime(n)^(1+1/n)) - prime(n+1).
%C A246777 a(1) > 0 and a(n) >= 0 for n < 76; this implies "if p=p(k) is in the sequence A002386 and p <= 1425172824437699411 then p(k+1)^(1/(k+1)) < p(k)^(1/k)."
%H A246777 A. Kourbatov, <a href="http://arxiv.org/abs/1503.01744">Verification of the Firoozbakht conjecture for primes up to four quintillion</a>, arXiv:1503.01744 [math.NT], 2015
%H A246777 A. Kourbatov, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Kourbatov/kourb7.html">Upper bounds for prime gaps related to Firoozbakht's conjecture</a>, J. Int. Seq. 18 (2015) 15.11.2
%H A246777 Wikipedia, <a href="http://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture">Firoozbakht's Conjecture</a>
%F A246777 a(n) = A246776(A005669(n)).
%t A246777 f[n_] := Block[{d, i, j, m = 0}, Reap@ For[i = 1, i <= n, i++, d = Prime[i + 1] - Prime@ i; If[d > m, m = d; Sow@ i, False]] // Flatten // Rest] (* A005669 *); g[n_] := Floor[Prime[n]^(1 + 1/n)] - Prime[n + 1] (* A246776 *); g@ f@ 100000; (* _Michael De Vlieger_, Mar 24 2015, with code from A246776 by _Farideh Firoozbakht_ *)
%Y A246777 Cf. A000040, A005250, A005669, A002386, A246776, A246778, A246779, A246789.
%K A246777 nonn
%O A246777 1,4
%A A246777 _Farideh Firoozbakht_, Sep 30 2014