login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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(n-d)) != 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

Juri-Stepan Gerasimov, Mar 15 2017

EXTENSIONS

Corrected by Charles R Greathouse IV, Mar 15 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified February 23 23:30 EST 2018. Contains 299595 sequences. (Running on oeis4.)