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A031926 Lower prime of a difference of 8 between consecutive primes. 19
89, 359, 389, 401, 449, 479, 491, 683, 701, 719, 743, 761, 911, 929, 983, 1109, 1163, 1193, 1373, 1439, 1523, 1559, 1571, 1733, 1823, 1979, 2003, 2153, 2213, 2243, 2273, 2459, 2531, 2609, 2663, 2699, 2741, 2843, 2879, 2909, 3011, 3041 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture: The sequence is infinite and for every n, a(n+1) < a(n)^(1+1/n). Namely 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

MAPLE

for i from 1 to 446 do if ithprime(i+1) = ithprime(i) + 8 then print({ithprime(i)}); fi; od; # Zerinvary Lajos, Mar 19 2007

p:=ithprime; nx:=nextprime; f:=proc(d) global p, nx; local i, t0, n; t0:=[]; for n from 1 to 100000 do i:=p(n); if nx(i)-i=d then t0:=[op(t0), i]; fi; od: t0; end; f(8); # N. J. A. Sloane, Jan 17 2012

MATHEMATICA

Transpose[Select[Partition[Prime[Range[500]], 2, 1], Last[#] - First[#] == 8 &]][[1]] (* Bruno Berselli, Apr 09 2013 *)

PROG

(MAGMA) [p: p in PrimesUpTo(4000) | NextPrime(p)-p eq 8]; // Bruno Berselli, Apr 09 2013

(PARI) is_A031926(p)={precprime(p-1)==p-8 && isprime(p)} \\ - M. F. Hasler, Apr 20 2013

(PARI) q=0; forprime(p=1, 5000, q+8==(q=p)&&print1(p-8", ")) \\ - M. F. Hasler, Apr 20 2013

CROSSREFS

Cf. A023202.

Sequence in context: A142685 A140772 A142292 * A132253 A288024 A118922

Adjacent sequences:  A031923 A031924 A031925 * A031927 A031928 A031929

KEYWORD

nonn

AUTHOR

Jeff Burch

STATUS

approved

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Last modified November 21 06:31 EST 2017. Contains 294989 sequences.