

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
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OFFSET

1,3


COMMENTS

This is the complement of A068499 (except that both include 1 as a term).
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
A166460: k1 is even and composite : present
(ii) If k is even and k+1 is prime,
A068499: k+1 does not divide k! : present
(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.
k+1 divides k! : absent
A166460: k+1 is composite : present
(End)


LINKS



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



CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



