A163769 Primes p such that 2*p+3 is not prime.

3, 11, 23, 31, 37, 41, 59, 61, 71, 79, 83, 101, 103, 107, 109, 131, 149, 151, 163, 179, 181, 191, 211, 233, 239, 241, 251, 257, 263, 271, 281, 293, 311, 313, 317, 331, 347, 359, 367, 373, 389, 401, 419, 421, 431, 433, 443, 449, 457, 461, 479, 491, 499, 521

Offset

1,1

Comments

All those p appear in A144562. [Proof: since 2p+3 is odd and not prime, it can be written as a product of two odd numbers, 2p+3=(2k+1)*(2s+1), therefore p=2ks+k+s-1. - R. J. Mathar, Aug 06 2009]

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Formula

A153238 INTERSECT A000040. - R. J. Mathar, Aug 05 2009

A000040 \ A023204. - R. J. Mathar, Aug 05 2009

Example

3 is in the sequence because 2*3+3=9 is composite; 23 is in the sequence because 2*23+3=49 is composite.

Mathematica

Select[Prime[Range[200]], !PrimeQ[2#+3]&] (* Harvey P. Dale, Feb 02 2012 *)

Prog

(Magma) [p: p in PrimesUpTo(700) | not IsPrime(2*p+3)]; // Vincenzo Librandi, Apr 08 2013

Crossrefs

Cf. A144562.

Sequence in context: A141226 A049491 A000355 * A100860 A018630 A163780

Adjacent sequences: A163766 A163767 A163768 * A163770 A163771 A163772

Keyword

nonn,easy

Author

Vincenzo Librandi, Aug 04 2009

Extensions

Entries checked - R. J. Mathar, Aug 06 2009

Status

approved