Search: id:A049591
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%I A049591
%S A049591 7,13,19,23,31,37,43,47,53,61,67,73,79,83,89,97,103,109,113,127,131,
%T A049591 139,151,157,163,167,173,181,193,199,211,223,229,233,241,251,257,263,
%U A049591 271,277,283,293,307,313,317,331,337,349,353,359,367,373,379,383,389
%N A049591 Odd primes p such that p+2 is composite.
%C A049591 Primes p such that nextprime(p)-p >= 4.
%C A049591 Primes p such that p+2 divides (p-1)!.
%C A049591 Odd primes n such that n!*B(n+1) is an integer, where B(k) are the Bernoulli 
               numbers. - Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 06 2002
%C A049591 Sequence appears also to give all n>1 such that there is no prime p satisfying 
               the inequality n<p<n+tau(n)^2 where tau(n)=A000005(n). - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Apr 13 2002
%C A049591 Conjecture: start from any initial value f(1)>=2 and define f(n) to be 
               the largest prime factor of f(1)+f(2)+...+f(n-1) then f(n)=n/2+O(log(n)) 
               and there are infinitely primes p such that f(2p)=p. Conjecture: 
               current sequence gives primes satisfying f(2p)=p when f(1)=3. - Benoit 
               Cloitre (benoit7848c(AT)orange.fr), Jun 04 2003
%D A049591 K. Soundararajan, Small gaps bewteen prime numbers: the work of Goldston-Pintz-Yildirim, 
               Bull. Amer. Math. Soc., 44 (2007), 1-18.
%H A049591 <a href="Sindx_Pri.html#gaps">Index entries for primes, gaps between</
               a>
%e A049591 13 is here because it is prime and 15 is composite. Also 15 divides 12!.
%p A049591 d:=4; M:=1000; t0:=[]; for n from 1 to M do p:=ithprime(n); if nextprime(p) 
               - p >= d then t0:=[op(t0),p]; fi; od: t0;
%Y A049591 Cf. A067774.
%Y A049591 Cf. A105399.
%Y A049591 Sequence in context: A109369 A088982 A033561 this_sequence A058620 A038910 
               A035497
%Y A049591 Adjacent sequences: A049588 A049589 A049590 this_sequence A049592 A049593 
               A049594
%K A049591 nonn
%O A049591 1,1
%A A049591 Labos E. (labos(AT)ana.sote.hu)
%E A049591 More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 04 2003
%E A049591 Edited by Don Reble (djr(AT)nk.ca), Dec 20 2006

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