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

1,2

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

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

Example

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.

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 *)

Prog

(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)
(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

Crossrefs

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

Sequence in context: A336892 A301905 A167321 * A116118 A038314 A119225

Adjacent sequences: A258481 A258482 A258483 * A258485 A258486 A258487

Keyword

nonn,base

Author

Pieter Post, May 31 2015

Extensions

More terms from Giovanni Resta, Jun 01 2015

Status

approved