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

1, 10, 12, 100, 101, 111, 1000, 1010, 1033, 1100, 2112, 4624, 10000, 10001, 11101, 20102, 31301, 100000, 100010, 100011, 100100, 100101, 100110, 101000, 101001, 101010, 101100, 101110, 101111, 101121, 110000, 110001, 110010, 110100, 110110, 110111, 111000

Offset: 1

Author

Pieter Post, May 31 2015

Keywords

• nonn
• base

Comments

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

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

Examples

			12 = 3^1 + 3^2;
31301 = 25^3 + 25^1 + 25^3 + 25^0 + 25^1;
595968 = 4^5 + 4^9 + 4^5 + 4^9 + 4^6 + 4^8;
13177388 = 7^1 + 7^3 + 7^1 + 7^7 + 7^7 + 7^3 + 7^8 + 7^8.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..956 (terms < 10^12)
• Giovanni Resta, Table of a(1..956) values and corresponding bases

Crossrefs

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

Programs

Mathematica

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 *)

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

Python

def moda(n,a,m):
    kk = 0
    while n > 0:
        na=int(n%m)
        kk= kk+a**na
        n =int(n//m)
    return kk
for c in range (1, 10**8):
    for a in range (1,20):
        if  c==moda(c,a,10):
            print (a,c)

Extensions

More terms from Giovanni Resta, Jun 01 2015