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A031924 Lower prime of a difference of 6 between consecutive primes. 42
23, 31, 47, 53, 61, 73, 83, 131, 151, 157, 167, 173, 233, 251, 257, 263, 271, 331, 353, 367, 373, 383, 433, 443, 503, 541, 557, 563, 571, 587, 593, 601, 607, 647, 653, 677, 727, 733, 751, 941, 947, 971, 977, 991, 1013, 1033, 1063, 1097, 1103 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: The sequence is infinite and for every n >= 7746, a(n+1) < a(n)^(1+1/n). Namely for n >= 7746, a(n)^(1/n) is a strictly decreasing function of n (See comment lines of the sequence A248855). - Jahangeer Kholdi and Farideh Firoozbakht, Nov 29 2014

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Index entries for primes, gaps between

EXAMPLE

23 is a term as the next prime 29 = 23 + 6.

MAPLE

A031924 := proc(n)

    option remember;

    if n = 1 then

        return 23;

    else

        p := nextprime(procname(n-1)) ;

        q := nextprime(p) ;

        while q-p <> 6 do

            p := q ;

            q := nextprime(p) ;

        end do:

        return p;

    end if;

end proc: # R. J. Mathar, Jan 23 2013

MATHEMATICA

Transpose[Select[Partition[Prime[Range[200]], 2, 1], Last[#] - First[#] == 6 &]][[1]] (* Bruno Berselli, Apr 09 2013 *)

PROG

(PARI) is(n)=isprime(n)&&nextprime(n+1)-n==6 \\ Charles R Greathouse IV, Mar 21 2013

(MAGMA) [p: p in PrimesUpTo(1200) | NextPrime(p)-p eq 6]; // Bruno Berselli, Apr 09 2013

CROSSREFS

Cf. A031925; A031924 and A007529 together give A023201.

Sequence in context: A124582 A130796 A258578 * A257528 A240886 A162587

Adjacent sequences:  A031921 A031922 A031923 * A031925 A031926 A031927

KEYWORD

nonn

AUTHOR

Jeff Burch

STATUS

approved

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Last modified May 24 09:15 EDT 2017. Contains 286963 sequences.