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 A245396 #57 Oct 29 2018 05:39:44
%S A245396 3,5,7,11,17,19,23,23,31,37,41,47,53,53,59,67,73,73,83,83,89,89,97,
%T A245396 107,113,113,113,113,127,131,139,151,157,157,167,173,179,181,181,193,
%U A245396 199,199,211,211,211,223,233,241,251,251,257,263,263,277,283,283,293,293,293,307,307,317,331,337
%N A245396 Largest prime not exceeding prime(n)^(1 + 1/n).
%C A245396 Firoozbakht's conjecture, prime(n+1) < prime(n)^(1 + 1/n), is equivalent to a(n) > prime(n). See also A182134.
%C A245396 Here prime(n) = A000040(n). The conjecture is also equivalent to a(n) - prime(n) >= A001223(n), the n-th gap between primes. See also A246778(n) = floor(prime(n)^(1 + 1/n)) - prime(n).
%C A245396 It is also conjectured that the equality a(n) - prime(n) = A001223(n) holds only for n in the set {1, 2, 3, 4, 8}, see A246782. a(n) is also largest prime less than prime(n)^(1 + 1/n), since prime(n)^(1 + 1/n) is never prime. - _Farideh Firoozbakht_, Nov 03 2014
%C A245396 a(n) = A007917(A249669(n)) = A244365(n,A182134(n)) = A006530(A245722(n)). - _Reinhard Zumkeller_, Nov 18 2014
%H A245396 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 A245396 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 A245396 Nilotpal Kanti Sinha, <a href="http://arxiv.org/abs/1010.1399">On a new property of primes that leads to a generalization of Cramer's conjecture</a>, arXiv:1010.1399 [math.NT]
%H A245396 Wikipedia, <a href="http://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture">Firoozbakht's conjecture</a>
%F A245396 A245396 = A007917 o A249669, i.e., a(n) = A007917(A249669(n)). Although one could say "less than" in the definition of this sequence, one cannot use A151799 in this formula because for n = 2 and n = 4, one has a(n) = A249669(n).
%p A245396 seq(prevprime(ceil(ithprime(n)^(1+1/n))),n=1..100); # _Robert Israel_, Nov 03 2014
%t A245396 Table[NextPrime[Prime[n]^(1 + 1/n), -1], {n, 64}] (* _Farideh Firoozbakht_, Nov 03 2014 *)
%o A245396 (PARI) a(n)=precprime(prime(n)^(1+1/n))
%o A245396 (PARI) a(n)=precprime(sqrtnint(prime(n)^(n+1),n)) \\ _Charles R Greathouse IV_, Oct 29 2018
%o A245396 (Haskell)
%o A245396 a245396 n = a244365 n (a182134 n) -- _Reinhard Zumkeller_, Nov 16 2014
%Y A245396 Cf. A000040, A001223, A007917, A182134, A246778, A249669.
%Y A245396 Cf. A244365.
%K A245396 nonn
%O A245396 1,1
%A A245396 _M. F. Hasler_, Nov 03 2014