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%I #47 Mar 23 2017 20:31:54
%S 1,9387629,18276717,40036062,252447645,293291802,319596455,327091015,
%T 401241904,421675344,471333967,483656680,1059439524,1162179372,
%U 1651177394,2339341839,2423329650,2596829984,2749510742,2903809499,2941064795,2956438949
%N Numbers n such that (n+1)^k + (-n)^k is prime for each k = 2, 3, 4, 5, 7, and 8.
%C 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)).
%e 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.
%Y Cf. A027862, A128780.
%K nonn
%O 1,2
%A _Altug Alkan_ and _Thomas Ordowski_, Feb 27 2017
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