%I A020497
%S A020497 1,3,7,9,13,17,21,27,31,33,37,43,49,51,57,61,67,71,77,81,85,91,95,101,
%T A020497 111,115,121,127,131,137,141,147,153,157,159,163,169,177,183,187,189,197,
%U A020497 201,211,213,217,227,237,241,247,253,255,265,271,273,279,283,289,301,305
%N A020497 a(n) is the minimal y such that n primes occur infinitely often among 
               (x+1, ..., x+y), i.e. pi(x+y)-pi(x) >= n for infinitely many x.
%C A020497 A020497(n) purportedly gives the least k with c(k) = n, where c()=A023193; 
               that is, A020497 should be the "least inverse" of A023193.
%C A020497 My web page extends the sequence to rho(305)=2047 and also gives a super-dense 
               occurrence at rho(592)=4333 when pi(4333)=591 - the first known occurrence. 
               - Thomas J Engelsma (tom(AT)opertech.com), Feb 16 2004
%C A020497 Tomas Oliveira e Silva (see link) has a table extending to n = 1000.
%D A020497 R. K. Guy, Unsolved Problems in Number Theory, (2nd edition, Springer, 
               1994), Section A9.
%D A020497 H. Smith, "On a generalization of the prime pair problem", Math. Comp., 
               11 (1957) 249-254.
%H A020497 T. D. Noe, <a href="b020497.txt">Table of n, a(n) for n=1..672</a> (from 
               Engelsma's data)
%H A020497 Thomas J. Engelsma, <a href="http://www.opertech.com/primes/k-tuples.html">
               Permissible Patterns</a>.
%H A020497 T. Forbes, <a href="http://anthony.d.forbes.googlepages.com/adf.htm">
               Prime k-tuplets</a>
%H A020497 Tomas Oliveira e Silva, <a href="http://www.ieeta.pt/~tos/apc.html">Admissible 
               prime constellations</a>
%H A020497 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               k-TupleConjecture.html">Prime k-Tuples Conjecture</a>.
%Y A020497 Equals A008407 + 1. First differences give A047947.
%Y A020497 Cf. A023193 (prime k-tuplet conjectures), A066081 (weaker binary conjectures).
%Y A020497 Sequence in context: A063204 A130568 A143803 this_sequence A023490 A032375 
               A089556
%Y A020497 Adjacent sequences: A020494 A020495 A020496 this_sequence A020498 A020499 
               A020500
%K A020497 nonn,nice
%O A020497 1,2
%A A020497 Robert G. Wilson v (rgwv(AT)rgwv.com), cet1(AT)cus.cam.ac.uk (Chris Thompson)
%E A020497 Corrected and extended by David W. Wilson (davidwwilson(AT)comcast.net).