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a(n) = prime(n)^(n+1) - prime(n+1)^n.
2

%I #30 Sep 08 2022 08:45:55

%S 1,2,282,2166,1400268,38610948,6081885702,244376712498,26919365237780,

%T 11380881478725028,609745162009089348,221005733915715119316,

%U 36210963070633268016918,2920403379610288252579938,493840220599528687495132964,183883082249204990404329361972

%N a(n) = prime(n)^(n+1) - prime(n+1)^n.

%C Firoozbakht conjecture: a(n) > 0 for all n. Let b(n) = a(n+1) - a(n). Conjecture: c(n) = b(n+1) - b(n) > 0 for all n. - _Thomas Ordowski_, May 07 2013

%H Amiram Eldar, <a href="/A182519/b182519.txt">Table of n, a(n) for n = 1..301</a>

%H A. Kourbatov, <a href="http://arxiv.org/abs/1503.01744">Verification of the Firoozbakht conjecture for primes up to four quintillion</a>, arXiv preprint arXiv:1503.01744 [math.NT], 2015

%H 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

%t Table[Prime[n]^(n+1) - Prime[n+1]^n, {n, 20}] (* _T. D. Noe_, May 03 2012 *)

%o (Magma) [NthPrime(n)^(n+1)-NthPrime(n+1)^n: n in [1..19]]; // _Vincenzo Librandi_, Nov 16 2016

%K nonn

%O 1,2

%A _Thomas Ordowski_, May 03 2012