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 A084745 Smallest prime of the form n^k - k, or 0 if no such prime exists. 3

%I

%S 2,2,3,23,5,47,7,79,997,5559917313492231463,11,167,13,223,4093,

%T 24137563,17,359,19,439,

%U 10947877107572929152919737180202022857988400441953615831

%N Smallest prime of the form n^k - k, or 0 if no such prime exists.

%C a(11) > 379749833583227. Conjecture: No entry is zero.

%C a(23) is 150 digits long and too long to include. - Alec Mihailovs (Alec(AT)Mihailovs.com), Jun 16 2003

%C If n-1 is a prime then a(n)=n-1. - _Farideh Firoozbakht_, Aug 09 2014

%H Michel Marcus, <a href="/A084745/b084745.txt">Table of n, a(n) for n = 2..35</a>

%F a(n) = n^A084746(n) - A084746(n). - _Michel Marcus_, Aug 09 2014

%e a(7) = 47 = 7^2 - 2.

%p a := proc(n) local k; k := 1; while not isprime(n^k-k) do k := k+1 od; n^k-k end: seq(a(n),n=2..35);

%t sp[n_]:=Module[{k=1},While[!PrimeQ[n^k-k],k++];n^k-k]; Array[sp,21,2] (* _Harvey P. Dale_, Jul 22 2021 *)

%o a(n)=k=1;while(!ispseudoprime(n^k-k),k++);return(n^k-k)

%o vector(20, n, a(n+1)) \\ _Derek Orr_, Aug 08 2014

%Y Cf. A084746.

%K nonn

%O 2,1

%A _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 15 2003

%E More terms from Alec Mihailovs (Alec(AT)Mihailovs.com), Jun 16 2003

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Last modified January 28 04:11 EST 2022. Contains 350654 sequences. (Running on oeis4.)