Re Composites Between Adjacent Primes

[N. J. A. Sloane]

My last message was truncated

let me try again

as a followup to this discussion
from earlier this month i am adding two seqs:

%I A114331
%S A114331 4,6,10,12,14,18,22,26,30,34,38,42,46,51,58,60,62,69,72,74,82,86,94,
%T A114331 99,102,106,108,111,122,129,134,138,146,150,155,158,166,172,178,180,
%U A114331 183,192,194,198,206,218,226,228,232,237,240,249,254,262,267,270
%N A114331 Observe that A052248(n) = greatest prime divisor q (say) of all composite num\
bers between p = prime(n) and next prime. There is only one composite number in this ran\
ge which is divisible by q. Sequence lists these composite numbers.
%C A114331 The uniqueness follows from Bertrand's Postulate. - Franklin T. Adams-Watters
%H A114331 Eric Weisstein, <a href="http://mathworld.wolfram.com/BertrandsPostulate.h
tml">Bertrand's Postulate</a>
%O A114331 2,1
%Y A114331 Cf. A052248, A114349.
%K A114331 nonn
%A A114331 njas, based on correspondence from Leroy Quet and Hugo Pfoertner, Feb 22 2006


%I A114349
%S A114349 2,2,2,4,2,6,2,2,6,2,2,6,2,3,2,12,2,3,24,2,2,2,2,9,6,2,3,3,2,3,2,6,
%T A114349 2,30,5,2,2,4,2,36,3,64,2,18,2,2,2,12,8,3,48,3,2,2,3,54,2,2,6,3,2,3,
%U A114349 24,2,2,2,2,12,27,2,2,7,8,2,2,2,2,4,3,60,2,144,4,26,2,2,2,42,2,2,2
%N A114349 Terms of A114331 divided by the appropriate prime (q) in A052248.
%O A114349 2,1
%K A114349 nonn
%A A114349 njas, based on correspondence from Leroy Quet and Hugo Pfoertner, Feb 22 2006

NJAS