A073499 Numbers k such that k^(k+1) + (k+1)^k is prime.
1, 2, 80, 342, 848, 1194, 2658, 4790, 9376
Offset: 1
Examples
1^2 + 2^1 = 3 and 2^3 + 3^2 = 17 are the primes corresponding to the first two terms. The next five terms correspond to primes of 155, 870, 2487, 3678 and 9106 decimal digits.
Links
- P. Leyland, Primes and Strong Pseudoprimes of the form x^y + y^x - The numbers corresponding to the first 7 terms had been proved prime by 2005.
Programs
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Mathematica
Do[ If[ PrimeQ[n^(n + 1) + (n + 1)^n], Print[n]], {n, 1, 1650}] -
PARI
for(n=1,1650, if(isprime((n^(n+1))+((n+1)^n)), print1(n,",")))
Extensions
Edited by Robert G. Wilson v, Aug 08 2002
a(7) from Charles R Greathouse IV, Jan 13 2012
a(8) from Charles R Greathouse IV, Jan 17 2012
a(9) found by Alexander Adamchuk, Apr 09 2007 and shown to be a(9) by Charles R Greathouse IV, Jan 27 2012
Comments