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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
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
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
KEYWORD
nonn,base
AUTHOR
Pieter Post, May 31 2015
EXTENSIONS
More terms from Giovanni Resta, Jun 01 2015
STATUS
approved