A067556 - OEIS

%I #10 Jun 16 2013 04:25:15

%S 7,357,17857,892857,44642857,2232,111607,5580357,279017857,

%T 13950892857,697544642857,34877232,1743861607,87193080357,

%U 4359654017857,217982700892857,10899135044642857,544956752232,27247837611607

%N Terms in the decimal expansion of 1/(7*2^n) before the block of decimals 142857 (the period of 1/7) appears.

%C Example : 1/(7*2^5) = 0.0044642857(142857...) where 142857 is the period of 1/7, hence a(5)=44642857.

%F a(n)=(1/7)*(5^n*10^(n mod 6)-1).

%F Empirical g.f.: x*(-44640625*x^5+43750000*x^4+875000*x^3+17500*x^2+350*x+7) / (15625*x^7-15625*x^6-x+1). - _Colin Barker_, Jun 16 2013

%o (PARI) a(n)=(1/7)*(5^n*10^(n%6)-1)

%o (PARI) a(n)=if(n<0,0,s=1;while(frac(10^s/7/2^n-1/7)>0,s++);floor(10^s/7/2^n))

%K nonn,base

%O 1,1

%A _Benoit Cloitre_, Jan 29 2002; revised Dec 11, 2004