Search: id:A087656
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%I A087656
%S A087656 1,2,2,4,3,6,3,4,5,10,4,12,7,6,4,16,5,18,6,8,11,22,5,8,13,6,8,28,7,30,
               5,
%T A087656 12,17,10,6,36,19,14,7,40,9,42,12,8,23,46,6,12,9,18,14,52,7,14,9,20,29,
%U A087656 58,8,60,31,10,6,16,13,66,18,24,11,70,7,72,37,10,20,16,15,78,8,8,41,82
%N A087656 Let f be defined on the rationals by f(p/q) =(p+1)/(q+1)=p_{1}/q_{1} 
               where (p_{1},q_{1})=1. Let f^k(p/q)=p_{k}/q_{k} where (p_{k},q_{k})=1. 
               Sequence gives least k such that p_{k}-q_{k} = 1 starting at n.
%C A087656 Proof that this is the same as A059975 except for offset, from Joseph 
               S. Myers (jsm(AT)polyomino.org.uk), Feb 21, 2004. Claim: a(n+1) = 
               A059975(n). If p is the least prime factor of n then the rule here 
               gives (n+1)/1 -> (n+2)/2 -> ... -> (n+p)/p = (n/p + 1)/1 so a(n+1) 
               = a(n/p + 1) + (p-1) and clearly A059975(n) = A059975(n/p) + (p-1). 
               The natural start for the induction is A059975(1) = a(2) = 0 (one 
               place before the currently listed sequences start).
%F A087656 If p is prime a(p+1)=p-1; it appears that a(n)=(n-1)/2 iff n is in A079148 
               or in A053177.
%e A087656 6 ->(6+1)/(1+1)=7/2 ->(7+1)/(2+1)=8/3 ->(8+1)/(3+1)=9/4 ->(9+1)/(4+1)=2/
               1 and 2-1=1 hence a(6)=4
%t A087656 a(x)=if(x<0, 0, c=0; while(abs(numerator(x)-denominator(x)-1)>0, x=(numerator(x)+1)/
               (denominator(x)+1); c++); c)
%Y A087656 Same as A059975 apart from offset.
%Y A087656 Sequence in context: A076435 A156864 A059975 this_sequence A122811 A089173 
               A126090
%Y A087656 Adjacent sequences: A087653 A087654 A087655 this_sequence A087657 A087658 
               A087659
%K A087656 nonn
%O A087656 3,2
%A A087656 Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 04 2003

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