A175768 - OEIS

%I #27 Aug 03 2024 14:29:26

%S 5,13,17,29,37,41,53,61,73,89,97,101,109,113,137,149,157,163,173,181,

%T 193,197,229,233,241,257,269,271,277,281,293,313,317,337,349,353,373,

%U 379,389,397,401,409,421,433,449,457,461,487,509,521,541,557,569,577,593,601,613

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

%C Without the restriction on b, the sequence would be identical to A000040.

%H Seiichi Manyama, <a href="/A175768/b175768.txt">Table of n, a(n) for n = 1..10000</a>

%e For a(3), 4 * 2^2 + 1 = 17, which is prime.

%e From _Seiichi Manyama_, Mar 27 2018: (Start)

%e    n | a(n)

%e   ---+----------------------------------

%e    1 |   5 =  1 * 2^2 + 1.

%e    2 |  13 =  3 * 2^2 + 1.

%e    3 |  17 =  4 * 2^2 + 1.

%e    4 |  29 =  7 * 2^2 + 1.

%e    5 |  37 =  9 * 2^2 + 1.

%e    6 |  41 = 10 * 2^2 + 1.

%e    7 |  53 = 13 * 2^2 + 1.

%e    8 |  61 = 15 * 2^2 + 1.

%e    9 |  73 = 18 * 2^2 + 1.

%e   10 |  89 = 22 * 2^2 + 1.

%e   11 |  97 = 24 * 2^2 + 1.

%e   12 | 101 = 25 * 2^2 + 1.

%e   13 | 109 = 27 * 2^2 + 1 = 4 * 3^3 + 1. (End)

%t Take[ Select[ Union@ Flatten@ Table[ k*b^b + 1, {b, 2, 20}, {k, 148}], PrimeQ], 55] (* _Robert G. Wilson v_, Sep 01 2010 *)

%o (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 Cf. A000040, A002144, A180362, A285015.

%K easy,nonn

%O 1,1

%A Kevin Batista (kevin762401(AT)yahoo.com), Sep 01 2010

%E Corrected and edited by _Charles R Greathouse IV_, Sep 02 2010