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A066938 Primes of the form p*q+p+q, where p and q are primes. 12
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A275596 A158913 A363638 * A219602 A242260 A076812
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jan 24 2002
EXTENSIONS
Edited by Robert G. Wilson v, Feb 01 2002
STATUS
approved

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Last modified May 29 11:28 EDT 2024. Contains 372940 sequences. (Running on oeis4.)