cp's OEIS Frontend

A088323 Number of numbers b>1 such that n is a repunit in base b representation.

%I A088323 #8 Feb 16 2025 08:32:51
%S A088323 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,
%T A088323 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,
%U A088323 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
%N A088323 Number of numbers b>1 such that n is a repunit in base b representation.
%C A088323 is a(n) < 4 ?;
%C A088323 n>2: a(n) > 0 as n = (n-1)^1 + (n-1)^0.
%C A088323 a(A119598(n)) > 3; a(A053696(n)) > 2; a(A085104(n)) > 2. - _Reinhard Zumkeller_, Jan 22 2014
%H A088323 Reinhard Zumkeller, <a href="/A088323/b088323.txt">Table of n, a(n) for n = 2..10000</a>
%H A088323 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Repunit.html">Repunit</a>
%e A088323 a(31)=3: 31 = 2^4+2^3+2^2+2^1+2^0 = 5^2+5^1+5^0 = 30^1+30^0.
%o A088323 (Haskell)
%o A088323 a088323 n = sum $ map (f n) [2 .. n-1] where
%o A088323    f x b = if x == 0 then 1 else if d /= 1 then 0 else f x' b
%o A088323                                  where (x',d) = divMod x b
%o A088323 -- _Reinhard Zumkeller_, Jan 22 2014
%Y A088323 Cf. A000225, A003462, A002275, A068953.
%K A088323 nonn,base
%O A088323 2,6
%A A088323 _Reinhard Zumkeller_, Nov 06 2003
%E A088323 Example corrected by _Reinhard Zumkeller_, Jan 22 2014