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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 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

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