

A100317


Numbers k such that exactly one of k  1 and k + 1 is prime.


7



1, 2, 3, 8, 10, 14, 16, 20, 22, 24, 28, 32, 36, 38, 40, 44, 46, 48, 52, 54, 58, 62, 66, 68, 70, 74, 78, 80, 82, 84, 88, 90, 96, 98, 100, 104, 106, 110, 112, 114, 126, 128, 130, 132, 136, 140, 148, 152, 156, 158, 162, 164, 166, 168, 172, 174, 178, 182, 190, 194, 196, 200
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OFFSET

1,2


COMMENTS

Beginning with a(2) = 3, n such that exactly one of n  1 and n + 1 is composite.


LINKS



EXAMPLE

3 is in the sequence because 2 is prime but 4 is composite.
4 is not in the sequence because both 3 and 5 are prime.
5 is not in the sequence either because both 4 and 6 are composite.


MATHEMATICA

Select[Range[250], Xor[PrimeQ[#  1], PrimeQ[# + 1]] &] (* G. C. Greubel, Apr 25 2019 *)
Module[{nn=Table[If[PrimeQ[n], 1, 0], {n, 0, 220}], t1, t2}, t1=Mean/@ SequencePosition[ nn, {1, _, 0}]; t2=Mean/@SequencePosition[nn, {0, _, 1}]; Flatten[ Join[t1, t2]]//Sort]1 (* Harvey P. Dale, Jul 13 2019 *)


PROG

(PARI) for(n=1, 250, if(isprime(n1)+isprime(n+1)==1, print1(n, ", ")))
(Magma) [n: n in [1..250]  IsPrime(n1) xor IsPrime(n+1) ]; // G. C. Greubel, Apr 25 2019
(Sage) [n for n in (1..250) if (is_prime(n1) + is_prime(n+1) == 1)] # G. C. Greubel, Apr 25 2019


CROSSREFS

Cf. A100318 (at least one of n  1 and n + 1 is composite).


KEYWORD

nonn


AUTHOR



STATUS

approved



