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 A007693 Primes p such that 6*p + 1 is also prime. (Formerly M0656) 22
 2, 3, 5, 7, 11, 13, 17, 23, 37, 47, 61, 73, 83, 101, 103, 107, 131, 137, 151, 173, 181, 233, 241, 257, 263, 271, 277, 283, 293, 311, 313, 331, 347, 367, 373, 397, 443, 461, 467, 503, 557, 577, 593, 601, 607, 641, 653, 661, 683, 727, 751, 761, 773, 787, 797, 853 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Solutions of the equation (6*n+1)' + n' = 2, where n' is the arithmetic derivative of n. [Paolo P. Lava, Oct 31 2012] REFERENCES J. Roberts, Lure of the Integers, Math. Assoc. America, 1992, p. 27983 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Harvey P. Dale, Table of n, a(n) for n = 1..1000 Andrew Granville, Sophie Germain's theorem for prime pairs p, 6p+1, J. Number Theory 27 (1987), no. 1, 63-72. FORMULA a(n) = (A051644(n)-1)/6. MATHEMATICA Select[Prime@Range[150], PrimeQ[6# + 1] &] (* Ray Chandler, Mar 14 2007  *) PROG (MAGMA) [n: n in [0..1000] | IsPrime(n) and IsPrime(6*n+1)]; // Vincenzo Librandi, Nov 18 2010 CROSSREFS Cf. A002476, A016921, A024899, A051644, A091178. Prime terms of A024899. Sequence in context: A268812 A283562 A152245 * A174048 A249644 A103144 Adjacent sequences:  A007690 A007691 A007692 * A007694 A007695 A007696 KEYWORD nonn,easy AUTHOR EXTENSIONS Extended by Ray Chandler, Mar 14 2007 STATUS approved

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Last modified September 23 20:42 EDT 2021. Contains 347617 sequences. (Running on oeis4.)