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 A249669 #40 Sep 08 2022 08:46:10 %S A249669 4,5,8,11,17,19,25,27,32,40,42,49,54,56,60,67,74,76,83,87,89,96,100, %T A249669 107,116,120,122,126,128,132,148,152,159,160,171,173,179,186,190,196, %U A249669 203,204,215,217,221,223,236,249,253,255,259,265,267,278,284,290,296,298,304,308,310,321 %N A249669 a(n) = floor(prime(n)^(1+1/n)). %C A249669 Firoozbakht's conjecture (prime(n)^(1/n) is a decreasing function), is equivalent to say that prime(n+1) <= a(n). (One has equality for n=2 and n=4.) See also A182134 and A245396. %C A249669 This is not A059921 o A000040, i.e., a(n) != A059921(prime(n)), since the base is prime(n) but the exponent is n. %C A249669 A245396(n) = A007917(a(n)). - _Reinhard Zumkeller_, Nov 16 2014 %H A249669 Robert Israel, <a href="/A249669/b249669.txt">Table of n, a(n) for n = 1..10000</a> %H A249669 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 A249669 A. Kourbatov, <a href="http://arxiv.org/abs/1506.03042">Upper bounds for prime gaps related to Firoozbakht's conjecture</a>, arXiv:1506.03042 [math.NT], 2015 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Kourbatov/kourb7.html">J. Int. Seq. 18 (2015) 15.11.2</a> %H A249669 Wikipedia, <a href="http://en.wikipedia.org/wiki/Firoozbakht%E2%80%99s_conjecture">Firoozbakht's conjecture</a> %F A249669 a(n) = prime(n) + (log(prime(n)))^2 - log(prime(n)) + O(1), see arXiv:1506.03042, Theorem 5. - _Alexei Kourbatov_, Nov 26 2015 %p A249669 seq(floor(ithprime(n)^(1+1/n)), n=1..100); # _Robert Israel_, Nov 26 2015 %o A249669 (PARI) a(n)=prime(n)^(1+1/n)\1 %o A249669 (Magma) [Floor(NthPrime(n)^(1+1/n)): n in [1..70]]; // _Vincenzo Librandi_, Nov 04 2014 %o A249669 (Haskell) %o A249669 a249669 n = floor $ fromIntegral (a000040 n) ** (1 + recip (fromIntegral n)) %o A249669 -- _Reinhard Zumkeller_, Nov 16 2014 %Y A249669 Cf. A245396, A007917, A244365, A246778, A263023. %K A249669 nonn %O A249669 1,1 %A A249669 _M. F. Hasler_, Nov 03 2014