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
KEYWORD
nonn
AUTHOR
Robert G. Wilson v, Mar 22 2001
STATUS
approved