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

1,1

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A175384 A053689 A176462 * A190792 A137796 A125213

Adjacent sequences: A060251 A060252 A060253 * A060255 A060256 A060257

Keyword

nonn

Author

Robert G. Wilson v, Mar 22 2001

Status

approved