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A022004 Initial members of prime triples (p, p+2, p+6). 30
5, 11, 17, 41, 101, 107, 191, 227, 311, 347, 461, 641, 821, 857, 881, 1091, 1277, 1301, 1427, 1481, 1487, 1607, 1871, 1997, 2081, 2237, 2267, 2657, 2687, 3251, 3461, 3527, 3671, 3917, 4001, 4127, 4517, 4637, 4787, 4931, 4967, 5231, 5477 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Solutions of the equation n'+(n+2)'+(n+6)'=3, where n' is the arithmetic derivative of n. [Paolo P. Lava, Nov 09 2012]

Subsequence of A001359. - R. J. Mathar, Feb 10 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Prime Triplet.

T. Forbes, Prime k-tuplets

Thomas R. Nicely, Enumeration of the prime triplets (q,q+2,q+6) to 1e16.

P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 132, ex. 3.4.3. [Broken link?]

P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 132, ex. 3.4.3.

R. J. Mathar, Table of Prime Gap Constallations

MAPLE

A022004 := proc(n)

    if n= 1 then

        5;

    else

        for a from procname(n-1)+2 by 2 do

            if isprime(a) and isprime(a+2) and isprime(a+6) then

                return a;

            end if;

        end do:

    end if;

end proc: # R. J. Mathar, Jul 11 2012

MATHEMATICA

Select[Prime[Range[1000]], PrimeQ[#+2] && PrimeQ[#+6]&] (* Vladimir Joseph Stephan Orlovsky, Mar 30 2011*)

Transpose[Select[Partition[Prime[Range[1000]], 3, 1], Differences[#]=={2, 4}&]][[1]] (* Harvey P. Dale, Dec 24 2011 *)

PROG

(MAGMA) [ p: p in PrimesUpTo(10000) | IsPrime(p+2) and IsPrime(p+6) ] [From Vincenzo Librandi, Nov 19 2010]

(PARI) is(n)=isprime(n)&&isprime(n+2)&&isprime(n+6) \\ Charles R Greathouse IV, Jul 01 2013

CROSSREFS

Cf. A073648, A098412.

Sequence in context: A094205 A136091 A184968 * A172454 A162001 A171713

Adjacent sequences:  A022001 A022002 A022003 * A022005 A022006 A022007

KEYWORD

nonn,easy

AUTHOR

Warut Roonguthai

STATUS

approved

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Last modified December 20 07:03 EST 2014. Contains 252241 sequences.