cp's OEIS Frontend

A175768 Primes of the form k * b^b + 1, with b > 1.

%I A175768 #27 Aug 03 2024 14:29:26
%S A175768 5,13,17,29,37,41,53,61,73,89,97,101,109,113,137,149,157,163,173,181,
%T A175768 193,197,229,233,241,257,269,271,277,281,293,313,317,337,349,353,373,
%U A175768 379,389,397,401,409,421,433,449,457,461,487,509,521,541,557,569,577,593,601,613
%N A175768 Primes of the form k * b^b + 1, with b > 1.
%C A175768 Without the restriction on b, the sequence would be identical to A000040.
%H A175768 Seiichi Manyama, <a href="/A175768/b175768.txt">Table of n, a(n) for n = 1..10000</a>
%e A175768 For a(3), 4 * 2^2 + 1 = 17, which is prime.
%e A175768 From _Seiichi Manyama_, Mar 27 2018: (Start)
%e A175768    n | a(n)
%e A175768   ---+----------------------------------
%e A175768    1 |   5 =  1 * 2^2 + 1.
%e A175768    2 |  13 =  3 * 2^2 + 1.
%e A175768    3 |  17 =  4 * 2^2 + 1.
%e A175768    4 |  29 =  7 * 2^2 + 1.
%e A175768    5 |  37 =  9 * 2^2 + 1.
%e A175768    6 |  41 = 10 * 2^2 + 1.
%e A175768    7 |  53 = 13 * 2^2 + 1.
%e A175768    8 |  61 = 15 * 2^2 + 1.
%e A175768    9 |  73 = 18 * 2^2 + 1.
%e A175768   10 |  89 = 22 * 2^2 + 1.
%e A175768   11 |  97 = 24 * 2^2 + 1.
%e A175768   12 | 101 = 25 * 2^2 + 1.
%e A175768   13 | 109 = 27 * 2^2 + 1 = 4 * 3^3 + 1. (End)
%t A175768 Take[ Select[ Union@ Flatten@ Table[ k*b^b + 1, {b, 2, 20}, {k, 148}], PrimeQ], 55] (* _Robert G. Wilson v_, Sep 01 2010 *)
%o A175768 (PARI) isA175768(n)=if(!isprime(n),return(0)); if(n%4==1||n%27==1,return(1)); forprime(b=5,log(n)/log(7),if(n%(b^b)==1,return(1)));0 \\ _Charles R Greathouse IV_, Sep 02 2010
%Y A175768 Cf. A000040, A002144, A180362, A285015.
%K A175768 easy,nonn
%O A175768 1,1
%A A175768 Kevin Batista (kevin762401(AT)yahoo.com), Sep 01 2010
%E A175768 Corrected and edited by _Charles R Greathouse IV_, Sep 02 2010