Search: id:A069923
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%I A069923
%S A069923 2,2,2,3,3,3,3,4,2,5,3,5,5,4,7,9,4,5,5,7,3,4,7,3,7,6,8,6,5,8,4,6,10,3,
%T A069923 5,3,7,6,7,7,8,6,7,5,7,5,8,4,2,7,6,6,7,3,6,6,11,6,6,9,8,8,7,7,6,6,10,8,
%U A069923 7,10,9,7,5,5,9,6,8,11,9,5,8,6,10,9,5,9,12,6,7,4,7,6,9,8,5,7,6,7,3,4,8
%N A069923 Number of primes p such that 2^n<=p<=2^n+prime(n).
%C A069923 For any n>0 is there always at least one prime p such that 2^n<=p<=2^n+prime(n)? 
               (checked until n=250 ) In this case, that would be stronger than 
               the Schinzel conjecture : "for m >1 there's at least one prime p 
               such that m<=p<=m+ln(m)^2" since for n >2 prime(n)<ln(2^n)^2=n^2*ln(2).
%o A069923 (PARI) for(n=1,65,print1(sum(i=2^n,2^n+prime(n),isprime(i)),","))
%Y A069923 Cf. A014210.
%Y A069923 Sequence in context: A097561 A162345 A048689 this_sequence A095840 A131343 
               A089051
%Y A069923 Adjacent sequences: A069920 A069921 A069922 this_sequence A069924 A069925 
               A069926
%K A069923 easy,nonn
%O A069923 1,1
%A A069923 Benoit Cloitre (benoit7848c(AT)orange.fr), May 05 2002

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