A067556 Terms in the decimal expansion of 1/(7*2^n) before the block of decimals 142857 (the period of 1/7) appears.

7, 357, 17857, 892857, 44642857, 2232, 111607, 5580357, 279017857, 13950892857, 697544642857, 34877232, 1743861607, 87193080357, 4359654017857, 217982700892857, 10899135044642857, 544956752232, 27247837611607

Offset: 1

Author

Benoit Cloitre, Jan 29 2002; revised Dec 11, 2004

Keywords

• nonn
• base

Comments

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

Programs

PARI

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

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))

Formula

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

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