editing

approved

a(A119598(n)) > 3; a(A053696(n)) > 2; a(A085104(n)) > 2. - Reinhard Zumkeller, Jan 22 2014

A010051(a(n)) * A088323(a(n)) > 1. - Reinhard Zumkeller, Jan 22 2014

a(31)=3: 31 = 2^4+2^3+2^2+2^1+2^0 = 35^32+35^1+35^0 = 30^1+30^0.

a085104 a088323 n = a085104_list !! sum $ map (f n) [2 .. n-1)] where

a085104_list = filter ((> 1) . a088323) a000040_list

f x b = if x == 0 then 1 else if d /= 1 then 0 else f x' b

where (x', d) = divMod x b

Example corrected by Reinhard Zumkeller, Jan 22 2014

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>

A010051(a(n)) * A088323(a(n)) > 1. - Reinhard Zumkeller, Jan 22 2014

(Haskell)

a085104 n = a085104_list !! (n-1)

a085104_list = filter ((> 1) . a088323) a000040_list

-- Reinhard Zumkeller, Jan 22 2014

Reinhard Zumkeller, <a href="/A088323/b088323.txt">Table of n, a(n) for n = 2..10000</a>

approved

editing

_Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, Nov 06 2003

nonn,base,new

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystemsgmail.com), Nov 06 2003

Number of numbers b>1 such that n is a repunit in base b representation.

0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

2,6

is a(n) < 4 ?;

n>2: a(n) > 0 as n = (n-1)^1 + (n-1)^0.

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Repunit.html">Repunit</a>

a(31)=3: 31 = 2^4+2^3+2^2+2^1+2^0 = 3^3+3^1+3^0 = 30^1+30^0.

Cf. A000225, A003462, A002275, A068953.

nonn,base

Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 06 2003

approved