OFFSET
1,1
COMMENTS
For p not equal to q, either p*q or p+q is odd, so their sum is odd.
The representation is ambiguous, e.g. 2*7+2+7 = 23 = 3*5+3+5.
None of these primes are in A158913 since if p*q+p+q is a prime, then sigma(p*q+p+q) = sigma(p*q). - Amiram Eldar, Nov 15 2021
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
A054973(a(n)+1) >= 2. - Amiram Eldar, Nov 15 2021
EXAMPLE
59 is in the sequence because 59 = 2 * 19 + 2 + 19.
MATHEMATICA
nn = 1000; n2 = PrimePi[nn/3]; Select[Union[Flatten[Table[(Prime[i] + 1) (Prime[j] + 1) - 1, {i, n2}, {j, n2}]]], # <= nn && PrimeQ[#] &]
PROG
(Haskell)
a066938 n = a066938_list !! (n-1)
a066938_list = map a000040 $ filter ((> 0) . a067432) [1..]
-- Reinhard Zumkeller, Oct 23 2011
(PARI) is(n)=fordiv(n+1, d, my(p=d-1, q=(n+1)/d-1); if(isprime(p) && isprime(q), return(isprime(n)))); 0 \\ Charles R Greathouse IV, Jul 23 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 24 2002
EXTENSIONS
Edited by Robert G. Wilson v, Feb 01 2002
STATUS
approved