Search: id:A160434
Results 1-1 of 1 results found.

%I A160434
%S A160434 2,3,7,11,20,26,30,37,43,44,42,64,66,46,70,87,99,91,78,95,133,119,113,
%T A160434 133,121,132,134,151,129,204,221,164,176,162,177,169,172,207
%N A160434 a(n) is the least number k such that (k-th prime after A002110(n)+1)-A002110(n) 
               is not a prime
%C A160434 The conjecure on the fortunate numbers rephrased with a(n) is:
%C A160434 a(n)>=2 for all n>=0.
%C A160434 More generally, is a(n)>n+1 always true, or even a(n)>ln(n+1)*(n+1)?
%e A160434 a(3)=11: A002110(3)+1=2*3*5+1=31. The 11 primes after 31 are 37,41,43,
               47,53,59,61,67,71,73 and 79.
%e A160434 Subtracting 2*3*5=30 from each yields:
%e A160434 7,11,13,17,23,29,31,37,41,43,49.
%e A160434 These are primes except for the 11th value, which is 49=7^2.
%p A160434 a(n):=proc(n) option remember;local k: for k from 1 while isprime((nextprime@@k)(A002110(n)+1)-A002110(n)) 
               do od:
%p A160434 k; end;
%Y A160434 A002110, A005235, A160433, A002110
%Y A160434 Sequence in context: A055502 A003173 A159262 this_sequence A139630 A133044 
               A014529
%Y A160434 Adjacent sequences: A160431 A160432 A160433 this_sequence A160435 A160436 
               A160437
%K A160434 hard,more,nonn
%O A160434 0,1
%A A160434 Frederick Magata (frederick.magata(AT)web.de), May 13 2009

Search completed in 0.001 seconds