A172192 Numbers k such that k^6 - (k+1)^5 is prime.

4, 9, 10, 12, 14, 19, 29, 46, 57, 59, 66, 71, 72, 84, 85, 90, 95, 96, 97, 114, 119, 122, 155, 157, 190, 191, 204, 207, 212, 221, 222, 244, 251, 256, 276, 285, 286, 289, 294, 300, 301, 307, 319, 320, 337, 344, 355, 359, 380, 382, 392, 400, 411, 422, 426, 441, 451

Offset: 1

Author

Ulrich Krug (leuchtfeuer37(AT)gmx.de), Jan 29 2010

Keywords

• nonn
• easy

Comments

Corresponding primes are in A171771. Negative values of primes are obtained for 1 and 2.

Examples

			4^6-(4+1)^5 = 971 is prime, so 4 is in the sequence.
5^6-(5+1)^5 = 7849 = 47*167 is composite, so 5 is not in the sequence.
9^6-(9+1)^5 = 431441 is prime, so 9 is in the sequence.
		

Crossrefs

Cf. A171771, A002327 (primes of form n^2-n-1), A140719 (primes of form n^3-(n+1)^2), A087191 (primes of form n^4-(n+1)^3).

Programs

Magma

[ n: n in [1..460] | IsPrime(p) and p gt 0 where p is n^6-(n+1)^5 ];

Mathematica

Select[Range[3,500],PrimeQ[#^6-(#+1)^5]&] (* Harvey P. Dale, Apr 25 2011 *)

PARI

is(n)=isprime(n^6-(n+1)^5) \\ Charles R Greathouse IV, Jun 13 2017

Extensions

Edited, extended, non-specific references removed and MAGMA program added by Associate Editors OEIS, Mar 05 2010