A182519 a(n) = prime(n)^(n+1) - prime(n+1)^n.

1, 2, 282, 2166, 1400268, 38610948, 6081885702, 244376712498, 26919365237780, 11380881478725028, 609745162009089348, 221005733915715119316, 36210963070633268016918, 2920403379610288252579938, 493840220599528687495132964, 183883082249204990404329361972

Offset: 1

Author

Thomas Ordowski, May 03 2012

Keywords

• nonn

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..301
• A. Kourbatov, Verification of the Firoozbakht conjecture for primes up to four quintillion, arXiv preprint arXiv:1503.01744 [math.NT], 2015
• A. Kourbatov, Upper bounds for prime gaps related to Firoozbakht's conjecture, J. Int. Seq. 18 (2015) 15.11.2

Programs

Magma

[NthPrime(n)^(n+1)-NthPrime(n+1)^n: n in [1..19]]; // Vincenzo Librandi, Nov 16 2016

Mathematica

Table[Prime[n]^(n+1) - Prime[n+1]^n, {n, 20}] (* T. D. Noe, May 03 2012 *)