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 A166460 Numbers k such that k + (-1)^k is not prime. 2
 0, 1, 5, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 24, 25, 26, 27, 29, 31, 32, 33, 34, 35, 37, 38, 39, 41, 43, 44, 45, 47, 48, 49, 50, 51, 53, 54, 55, 56, 57, 59, 61, 62, 63, 64, 65, 67, 68, 69, 71, 73, 74, 75, 76, 77, 79, 80, 81, 83, 84, 85, 86, 87, 89, 90, 91, 92, 93, 94 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS This is the complement of A068499 (except that both include 1 as a term). From Don Reble, Aug 31 2021: (Start) Proof for all k except 0, 1, 3 with cases (i) If k is odd and >=5, then k+1 = 2*x, 2 < x < k, k! = k*...*x*...*2*1 A068499: k+1 divides k! : absent A166460: k-1 is even and composite : present (ii) If k is even and k+1 is prime, A068499: k+1 does not divide k! : present A166460: k+1 is prime : absent (iii) If k is even and k+1 = p^2 is the square of a (odd) prime, then k+1 >= 3p, k > 2p. A068499: k! = k*...*2p*...*p*...*1; k+1 divides k! : absent A166460: k+1 is composite : present (iv) If k is even and k+1 is composite but not the square of a prime, then there are two distinct factors x*y = k+1: 3 <= x < y = (k+1)/x < k. A068499: k! = k*...*y*...*x*...*1: k+1 divides k! : absent A166460: k+1 is composite : present (End) LINKS Michael De Vlieger, Table of n, a(n) for n = 1..10000 EXAMPLE 0 + (-1)^0 = 1 is not prime, which adds 0 to the sequence. 5 + (-1)^5 = 4 is not prime, which adds 5 to the sequence. MATHEMATICA Select[Range[0, 94], ! PrimeQ[# + (-1)^#] &] (* Michael De Vlieger, Sep 08 2021 *) CROSSREFS Cf. A072668, A141468, A060462, A118742, A068499. Sequence in context: A255922 A241028 A171097 * A118742 A122904 A104693 Adjacent sequences: A166457 A166458 A166459 * A166461 A166462 A166463 KEYWORD nonn,easy AUTHOR Juri-Stepan Gerasimov, Oct 14 2009 EXTENSIONS 0 added by R. J. Mathar, Oct 21 2009 STATUS approved

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Last modified December 9 13:48 EST 2023. Contains 367691 sequences. (Running on oeis4.)