A281570 Numbers n such that (n+1)^k + (-n)^k is prime for each k = 2, 3, 4, 5, 7, and 8.

1, 9387629, 18276717, 40036062, 252447645, 293291802, 319596455, 327091015, 401241904, 421675344, 471333967, 483656680, 1059439524, 1162179372, 1651177394, 2339341839, 2423329650, 2596829984, 2749510742, 2903809499, 2941064795, 2956438949

Offset: 1

Author

Altug Alkan and Thomas Ordowski, Feb 27 2017

Keywords

• nonn

Comments

For k = 6 and 9, (n+1)^k + (-n)^k is always composite (i.e. (n+1)^6 + (-n)^6 = (2*n^2+2*n+1)*(n^4+2*n^3+5*n^2+4*n+1), (n+1)^9 + (-n)^9 = (3*n^2+3*n+1)*(3*n^6+9*n^5+18*n^4+21*n^3+15*n^2+6*n+1)).

Examples

			9387629 is a term because 9387630^3 - 9387629^3, 9387630^5 - 9387629^5, 9387630^7 - 9387629^7 and 9387629^2 + 9387630^2, 9387629^4 + 9387630^4, 9387629^8 + 9387630^8 are prime numbers.
		

Crossrefs

Cf. A027862, A128780.