A050621 Smallest n-digit number divisible by 2^n.

2, 12, 104, 1008, 10016, 100032, 1000064, 10000128, 100000256, 1000000512, 10000001024, 100000002048, 1000000004096, 10000000008192, 100000000016384, 1000000000032768, 10000000000065536, 100000000000131072

Offset: 1

Author

Patrick De Geest, Jun 15 1999

Keywords

• nonn
• base
• easy

Comments

Quotients arising from this sequence give A034478 ((5^(n-1)+1)/2).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Index entries for linear recurrences with constant coefficients, signature (12,-20).

Crossrefs

Cf. A035014, A034478, A050622.

Programs

Magma

[2^(n-1)+10^(n-1): n in [1..21]]; // Vincenzo Librandi, Sep 12 2014

Mathematica

CoefficientList[Series[2 (1 - 6 x)/((1 - 2 x) (1 - 10 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Sep 12 2014 *)

PARI

a(n) = 10^(n-1) + 2^(n-1) \\ Charles R Greathouse IV, Jun 11 2015

Formula

a(n) = 10^(n-1) + 2^(n-1).

G.f.: Q(0) where Q(k)= 1 + 5^k/(1 - 2*x/(2*x + 5^k/Q(k+1) )); (continued fraction ). - Sergei N. Gladkovskii, Apr 10 2013

G.f.: 2*x*(1-6*x)/((1-2*x)*(1-10*x)). - Vincenzo Librandi, Sep 12 2014

a(n) = 12*a(n-1) - 20*a(n-2) for n>1. - Vincenzo Librandi, Sep 12 2014