

A283022


Numbers n such that the number of primes of the form n  x is not equal to the number of primes of the form n + y where x, y are divisors of n.


1



1, 2, 3, 4, 6, 8, 14, 16, 20, 24, 26, 28, 32, 34, 36, 38, 40, 44, 48, 52, 54, 62, 66, 68, 70, 74, 78, 80, 84, 86, 88, 90, 94, 96, 98, 100, 104, 110, 112, 114, 118, 122, 126, 128, 130, 132, 134, 136, 140, 142, 146, 148, 152, 156, 158, 162, 164, 168, 172, 174, 182, 190, 194, 196, 200, 202
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OFFSET

1,2


COMMENTS

Terms are all even for n > 3.
Sophie Germain primes > 3 such that the number of primes of the form 2p  x is equal to the number of primes of the form 2p + y where x, y are divisors of 2p.


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000


EXAMPLE

3 is in this sequence because 3  1 = 2 is prime and 3  3 = 0, but 3 + 1 = 4 and 3 + 3 = 6, where 1, 3 are divisors of 3 and 0, 4, 6 are nonprimes.


MATHEMATICA

p[n_]:=If[PrimeQ[n], 1, 0]; Select[Range@ 202, Sum[p[#  d], {d, Divisors[Factor[#]]}] != Sum[p[# + d], {d, Divisors[Factor[#]]}] &] (* Indranil Ghosh, Mar 15 2017 *)


PROG

(PARI) is(n)=my(f=factor(n)); sumdiv(f, d, isprime(nd)) != sumdiv(f, d, isprime(n+d)) \\ Charles R Greathouse IV, Mar 15 2017


CROSSREFS

Cf. A005384 (Sophie Germain primes), A005382 (primes p such that number of primes of the form 2p  m is equal to exactly two, where m is divisor of p).
Sequence in context: A155051 A018137 A084239 * A219186 A049708 A000031
Adjacent sequences: A283019 A283020 A283021 * A283023 A283024 A283025


KEYWORD

nonn


AUTHOR

JuriStepan Gerasimov, Mar 15 2017


EXTENSIONS

Corrected by Charles R Greathouse IV, Mar 15 2017


STATUS

approved



