

A060254


Primes which are the sum of two consecutive composite numbers.


22



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
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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 p1 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.  JuriStepan 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



