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

5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 163, 173, 181, 193, 197, 229, 233, 241, 257, 269, 271, 277, 281, 293, 313, 317, 337, 349, 353, 373, 379, 389, 397, 401, 409, 421, 433, 449, 457, 461, 487, 509, 521, 541, 557, 569, 577, 593, 601, 613

Offset: 1

Author

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

Keywords

• easy
• nonn

Comments

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

Examples

			For a(3), 4 * 2^2 + 1 = 17, which is prime.
From _Seiichi Manyama_, Mar 27 2018: (Start)
   n | a(n)
  ---+----------------------------------
   1 |   5 =  1 * 2^2 + 1.
   2 |  13 =  3 * 2^2 + 1.
   3 |  17 =  4 * 2^2 + 1.
   4 |  29 =  7 * 2^2 + 1.
   5 |  37 =  9 * 2^2 + 1.
   6 |  41 = 10 * 2^2 + 1.
   7 |  53 = 13 * 2^2 + 1.
   8 |  61 = 15 * 2^2 + 1.
   9 |  73 = 18 * 2^2 + 1.
  10 |  89 = 22 * 2^2 + 1.
  11 |  97 = 24 * 2^2 + 1.
  12 | 101 = 25 * 2^2 + 1.
  13 | 109 = 27 * 2^2 + 1 = 4 * 3^3 + 1. (End)
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A002144, A180362, A285015.

Programs

Mathematica

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

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

Extensions

Corrected and edited by Charles R Greathouse IV, Sep 02 2010