A258484 - OEIS

%I #23 Mar 11 2024 01:44:23

%S 1,10,12,100,101,111,1000,1010,1033,1100,2112,4624,10000,10001,11101,

%T 20102,31301,100000,100010,100011,100100,100101,100110,101000,101001,

%U 101010,101100,101110,101111,101121,110000,110001,110010,110100,110110,110111,111000

%N Numbers m such that m equals a fixed number raised to the powers of the digits.

%C Let m = abcde... and z is a fixed radix -> m = z^a +z^b +z^c +z^d +z^e...

%C A number m made of k ones and h zeros is a member if m-h is divisible by k. Several other large members exist, including 12095925296900865188 (base = 113) and 115330163577499130079377256005 (base = 1500). - _Giovanni Resta_, Jun 01 2015

%H Giovanni Resta, <a href="/A258484/b258484.txt">Table of n, a(n) for n = 1..956</a> (terms < 10^12)

%H Giovanni Resta, <a href="/A258484/a258484.txt">Table of a(1..956) values and corresponding bases</a>

%e 12 = 3^1 + 3^2;

%e 31301 = 25^3 + 25^1 + 25^3 + 25^0 + 25^1;

%e 595968 = 4^5 + 4^9 + 4^5 + 4^9 + 4^6 + 4^8;

%e 13177388 = 7^1 + 7^3 + 7^1 + 7^7 + 7^7 + 7^3 + 7^8 + 7^8.

%t okQ[v_] := Block[{b, d=IntegerDigits@ v, y, t}, t = Last@ Tally@ Sort@d; b = Floor[ (v/t[[2]]) ^ (1/t[[1]])]; While[(y = Total[b^d]) > v, b--]; v==y]; Select[Range[10^5],okQ] (* _Giovanni Resta_, Jun 01 2015 *)

%o (Python)

%o def moda(n,a,m):

%o ....kk = 0

%o ....while n > 0:

%o ........na=int(n%m)

%o ........kk= kk+a**na

%o ........n =int(n//m)

%o ....return kk

%o for c in range (1, 10**8):

%o ....for a in range (1,20):

%o ........if  c==moda(c,a,10):

%o ............print (a,c)

%o (PARI) for(n=1,10^5,d=digits(n);for(m=1,n,s=sum(i=1,#d,m^d[i]);if(s==n,print1(n,", ");break);if(s>n,break))) \\ _Derek Orr_, Jun 12 2015

%Y Cf. A005188, A023052, A257784, A257766, A257787, A257814.

%K nonn,base

%O 1,2

%A _Pieter Post_, May 31 2015

%E More terms from _Giovanni Resta_, Jun 01 2015