A066938 Primes of the form p*q+p+q, where p and q are primes.

11, 17, 23, 31, 41, 47, 53, 59, 71, 79, 83, 89, 107, 113, 127, 131, 151, 167, 179, 191, 227, 239, 251, 263, 269, 271, 293, 311, 359, 383, 419, 431, 439, 443, 449, 479, 491, 503, 521, 587, 593, 599, 607, 631, 647, 659, 683, 701, 719, 727, 743, 773, 809, 827

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.

Complement of A198273 with respect to A000040. - Reinhard Zumkeller, Oct 23 2011

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

A067432(A049084(a(n))) > 0. - Reinhard Zumkeller, Oct 23 2011

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

Cf. A054973, A067432, A072668, A072673, A088709, A158913, A198273, A198277.

Sequence in context: A275596 A158913 A363638 * A219602 A242260 A076812

Adjacent sequences: A066935 A066936 A066937 * A066939 A066940 A066941

Keyword

nonn

Author

Reinhard Zumkeller, Jan 24 2002

Extensions

Edited by Robert G. Wilson v, Feb 01 2002

Status

approved