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A031926
Lower prime of a difference of 8 between consecutive primes.
26
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
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved