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A258484 Numbers m such that m equals a fixed number raised to the powers of the digits. 2
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 (list; graph; refs; listen; history; text; internal format)
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.

MAPLE

P:=proc(n) local a, b, j, k; a:=convert(n, base, 10); b:=0; k:=0;

while b<n do k:=k+1; b:=add(k^a[j], j=1..nops(a)); od; if b=n then n;

fi; end: seq(P(i), i=1..111000); # Paolo P. Lava, May 09 2018

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: A241252 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

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Last modified February 19 04:05 EST 2020. Contains 332034 sequences. (Running on oeis4.)