A060254 Primes which are the sum of two consecutive composite numbers.

17, 19, 29, 31, 41, 43, 53, 67, 71, 79, 89, 97, 101, 103, 109, 113, 127, 131, 137, 139, 149, 151, 163, 173, 181, 191, 197, 199, 211, 223, 229, 233, 239, 241, 251, 257, 269, 271, 281, 283, 293, 307, 311, 317, 331, 337, 349, 353, 367, 373, 379, 389, 401, 409

Offset: 1

Author

Robert G. Wilson v, Mar 22 2001

Keywords

• nonn

Comments

For the smaller of the consecutive composite pair (p-+1)/2, see A096784

This sequence also contains exactly those odd primes p where neither p-1 nor p+1 is the product of exactly 2 (not necessarily distinct) primes. - Leroy Quet, Sep 09 2008

5 together with the prime numbers A060254=(5,17,19,29,31,41,43,53,..)=primes which are the sum of two consecutive nonprime numbers. - Juri-Stepan Gerasimov, Aug 30 2009

Conjecture: a(n) ~ n log n. - Charles R Greathouse IV, Apr 29 2015

Examples

			The prime 19 is an entry since it is the sum of 9=3^2 and 10=2*5.
		

Links

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

Crossrefs

Cf. A096783, A096784, A096785, A096786, A096787, A096788, A096677.

Programs

Mathematica

2Select[ Range[210], PrimeQ[ # ] == PrimeQ[ # + 1] == False && PrimeQ[2# + 1] == True &] + 1
Select[Total/@Partition[Select[Range[300],CompositeQ],2,1],PrimeQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 12 2019 *)

PARI

is(n)=!isprime(n\2) && !isprime(n\2+1) && isprime(n) \\ Charles R Greathouse IV, Apr 29 2015