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A258484 Numbers m such that m equals a fixed number raised to the powers of the digits.

%I A258484 #25 May 22 2025 10:21:43
%S A258484 1,10,12,100,101,111,1000,1010,1033,1100,2112,4624,10000,10001,11101,
%T A258484 20102,31301,100000,100010,100011,100100,100101,100110,101000,101001,
%U A258484 101010,101100,101110,101111,101121,110000,110001,110010,110100,110110,110111,111000
%N A258484 Numbers m such that m equals a fixed number raised to the powers of the digits.
%C A258484 Let m = abcde... and z is a fixed radix -> m = z^a +z^b +z^c +z^d +z^e...
%C A258484 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 A258484 Giovanni Resta, <a href="/A258484/b258484.txt">Table of n, a(n) for n = 1..956</a> (terms < 10^12)
%H A258484 Giovanni Resta, <a href="/A258484/a258484.txt">Table of a(1..956) values and corresponding bases</a>
%e A258484 12 = 3^1 + 3^2;
%e A258484 31301 = 25^3 + 25^1 + 25^3 + 25^0 + 25^1;
%e A258484 595968 = 4^5 + 4^9 + 4^5 + 4^9 + 4^6 + 4^8;
%e A258484 13177388 = 7^1 + 7^3 + 7^1 + 7^7 + 7^7 + 7^3 + 7^8 + 7^8.
%t A258484 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 A258484 (Python)
%o A258484 def moda(n,a,m):
%o A258484     kk = 0
%o A258484     while n > 0:
%o A258484         na=int(n%m)
%o A258484         kk= kk+a**na
%o A258484         n =int(n//m)
%o A258484     return kk
%o A258484 for c in range (1, 10**8):
%o A258484     for a in range (1,20):
%o A258484         if  c==moda(c,a,10):
%o A258484             print (a,c)
%o A258484 (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 A258484 Cf. A005188, A023052, A257784, A257766, A257787, A257814.
%K A258484 nonn,base
%O A258484 1,2
%A A258484 _Pieter Post_, May 31 2015
%E A258484 More terms from _Giovanni Resta_, Jun 01 2015