A113019 - OEIS

%I #17 Nov 17 2019 15:09:35

%S 1,1,1,1,1,1,1,1,1,1,2,4,8,16,32,64,128,256,512,2,4,8,16,32,64,128,

%T 256,512,2,4,8,16,32,64,128,256,512,2,4,8,16,32,64,128,256,512,2,4,8,

%U 16,32,64,128,256,512,2,4,8,16,32,64,128,256,512,2,4,8,16,32

%N (Number of digits of n) raised to the power of (the digital root of n).

%C n=1 and 32 are fixed points. Are there any others?

%C First occurrence of k: 1,10,100,11,10000,100000,1000000,12,101,1000000000, ..., . - _Robert G. Wilson v_

%H Nathaniel Johnston, <a href="/A113019/b113019.txt">Table of n, a(n) for n = 0..10000</a>

%F a(ijk...) [m digits ijk...] = m^(i+j+k+..[one digit])

%F a(n)=A055642(n)^A010888(n). - _Robert G. Wilson v_

%e a(0) = 1^0 = 1.

%e a(9) = 1^9 = 1.

%e a(10) = 2^(1+0) = 2.

%e a(89) = 2^(8+9=17=>1+7) = 2^8 = 256.

%p A113019 := proc(n) if(n=0)then return 1:fi: return length(n)^(((n-1) mod 9) + 1): end: seq(A113019(n),n=0..100); # _Nathaniel Johnston_, May 04 2011

%t f[n_] := If[n == 0, 1, Floor[ Log[10, 10n]]^(Mod[n - 1, 9] + 1)]; Table[ f[n], {n, 0, 73}] (* _Robert G. Wilson v_, Jan 04 2006 *)

%o (PARI) apply( A113019(n)=(logint(n+!n,10)+1)^((n-1)%9+1), [0..99]) \\ _M. F. Hasler_, Nov 17 2019

%Y Cf. A101337.

%K base,easy,nonn

%O 0,11

%A _Alexandre Wajnberg_, Jan 03 2006