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A007693 Numbers n such that n and 6n+1 are primes.
(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

N. J. A. Sloane, Robert G. Wilson v

EXTENSIONS

Extended by Ray Chandler, Mar 14 2007

STATUS

approved

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Last modified February 23 12:03 EST 2019. Contains 320431 sequences. (Running on oeis4.)