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 A246776 a(n) = floor(prime(n)^(1+1/n)) - prime(n+1). 7
 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, 15, 5, 17, 15, 20, 11, 20, 16, 16, 19, 17, 17, 22, 13, 22, 20, 22, 12, 13, 22, 24, 22, 20, 24, 16, 21, 21, 21, 25, 21, 23, 25, 17, 14, 25, 27, 24, 14, 23, 20, 28, 26 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS 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. A246777 is a hard subsequence of this sequence. 18 is not in the sequence. It seems that, 18 is the only nonnegative integer which is not in the sequence. REFERENCES Paulo Ribenboim, The little book Of bigger primes, second edition, Springer, 2004, p. 185. LINKS Carlos Rivera, Conjecture 30 A. Kourbatov, Verification of the Firoozbakht conjecture for primes up to four quintillion, arXiv:1503.01744 [math.NT], 2015 Alexei Kourbatov, Upper Bounds for Prime Gaps Related to Firoozbakhtâ€™s Conjecture, arXiv preprint, 2015. A. Kourbatov, Upper bounds for prime gaps related to Firoozbakht's conjecture, J. Int. Seq. 18 (2015) 15.11.2 Wikipedia, Prime gap. Wikipedia, Firoozbakht Conjecture. FORMULA a(n) = A249669(n) - A000040(n+1). - Reinhard Zumkeller, Nov 16 2014 MATHEMATICA Table[Floor[Prime[n]^(1+1/n)]-Prime[n+1], {n, 70}] PROG (Haskell) a246776 n = a249669 n - a000040 (n + 1) -- Reinhard Zumkeller, Nov 16 2014 CROSSREFS Cf. A000040, A001223, A005669, A246777, A246778. Cf. A249669. Sequence in context: A272101 A059853 A136527 * A138614 A161912 A162339 Adjacent sequences:  A246773 A246774 A246775 * A246777 A246778 A246779 KEYWORD nonn AUTHOR Farideh Firoozbakht, Sep 26 2014 STATUS approved

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Last modified September 19 11:06 EDT 2019. Contains 327192 sequences. (Running on oeis4.)