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A007693
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Numbers n such that n and 6n+1 are primes.
(Formerly M0656)
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17
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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;
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listen;
history;
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OFFSET
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1,1
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COMMENTS
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Solutions of the equation (6*n+1)' + n' = 2, where n' is the arithmetic derivative of n. [Paolo P. Lava, Oct 31 2012]
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REFERENCES
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Andrew Granville, Sophie Germain's theorem for prime pairs p, 6p+1, J. Number Theory 27 (1987), no. 1, 63-72.
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).
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = (A051644(n)-1)/6.
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MATHEMATICA
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Select[Prime@Range[150], PrimeQ[6# + 1] &] (*Chandler*)
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PROG
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(MAGMA) [n: n in [0..1000] | IsPrime(n) and IsPrime(6*n+1)] [V. Librandi, Nov 18 2010]
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CROSSREFS
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Cf. A002476, A016921, A024899, A051644, A091178.
Prime terms of A024899.
Sequence in context: A175584 A216823 A152245 * A174048 A103144 A105909
Adjacent sequences: A007690 A007691 A007692 * A007694 A007695 A007696
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane, Robert G. Wilson v
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EXTENSIONS
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Extended by Ray Chandler, Mar 14 2007
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STATUS
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approved
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