This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A246776 #45 May 27 2025 10:08:12
%S A246776 1,0,1,0,4,2,6,4,3,9,5,8,11,9,7,8,13,9,12,14,10,13,11,10,15,17,15,17,
%T A246776 15,5,17,15,20,11,20,16,16,19,17,17,22,13,22,20,22,12,13,22,24,22,20,
%U A246776 24,16,21,21,21,25,21,23,25,17,14,25,27,24,14,23,20,28,26
%N A246776 a(n) = floor(prime(n)^(1+1/n)) - prime(n+1).
%C A246776 The Firoozbakht Conjecture, "prime(n)^(1/n) is a strictly decreasing function of n" is true if and only if a(n) is nonnegative for all n, n>1.
%C A246776 A246777 is a hard subsequence of this sequence.
%C A246776 18 is not in the sequence. It seems that, 18 is the only nonnegative integer which is not in the sequence.
%D A246776 Paulo Ribenboim, The little book Of bigger primes, second edition, Springer, 2004, p. 185.
%H A246776 Alois P. Heinz, <a href="/A246776/b246776.txt">Table of n, a(n) for n = 1..10000</a> (first 4230 terms from Hal M. Switkay)
%H A246776 Carlos Rivera, <a href="http://www.primepuzzles.net/conjectures/conj_030.htm">Conjecture 30</a>
%H A246776 Alexei 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], 2015-2023.
%H A246776 Alexei Kourbatov, <a href="https://arxiv.org/abs/1506.03042">Upper Bounds for Prime Gaps Related to Firoozbakht’s Conjecture</a>, arXiv:1506.03042 [math.NT], 2015-2019.
%H A246776 Alexei 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 A246776 Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_gap">Prime gap</a>.
%H A246776 Wikipedia, <a href="http://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture">Firoozbakht Conjecture</a>.
%F A246776 a(n) = A249669(n) - A000040(n+1). - _Reinhard Zumkeller_, Nov 16 2014
%t A246776 Table[Floor[Prime[n]^(1+1/n)]-Prime[n+1],{n,70}]
%o A246776 (Haskell)
%o A246776 a246776 n = a249669 n - a000040 (n + 1)
%o A246776 -- _Reinhard Zumkeller_, Nov 16 2014
%Y A246776 Cf. A000040, A001223, A005669, A246777, A246778.
%Y A246776 Cf. A249669.
%K A246776 nonn
%O A246776 1,5
%A A246776 _Farideh Firoozbakht_, Sep 26 2014