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A060254
Primes which are the sum of two consecutive composite numbers.
23
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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Mar 22 2001
STATUS
approved