A003321 - OEIS

%I M5403 #44 Dec 11 2021 04:34:00

%S 2,0,153,1634,4150,548834,1741725,24678050,146511208,4679307774,

%T 32164049650,0,564240140138,28116440335967,0,4338281769391370,

%U 233411150132317,0,1517841543307505039,63105425988599693916

%N Smallest n-th order perfect digital invariant or PDI: smallest number > 1 equal to sum of n-th powers of its digits, or 0 if no such number exists.

%C Except for the initial term, this is the third column of A252648. - _M. F. Hasler_, Feb 16 2015

%C a(n) = 0 if n>1 and in A262094. - _Dmitry Kamenetsky_, Jun 05 2020

%D M. Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 249.

%D J. S. Madachy, Mathematics on Vacation, Thomas Nelson and Sons Ltd. 1966, p. 164.

%D J. S. Madachy, Madachy's Mathematical Recreations, Dover, p. 164.

%D C. A. Pickover, Keys to Infinity. New York: W. H. Freeman, pp. 169-170, 1995.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Joseph Myers, <a href="/A003321/b003321.txt">Table of n, a(n) for n=1..109</a>

%H L. E. Deimel, <a href="http://www.deimel.org/rec_math/DI_1.htm">Narcissistic Numbers</a>

%H H. Heinz, <a href="http://www.magic-squares.net/narciss.htm#PDIs">Narcissistic Numbers</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NarcissisticNumber.html">Narcissistic Number.</a>

%e 1^3 + 5^3 + 3^3 = 153.

%e 1*0^17 + 5*1^17 + 2*2^17 + 4*3^17 + 1*4^17 + 1*5^17 + 1*7^17 = 233411150132317.

%o (PARI) a(n)=m=1;while(m*9^n>=10^m,m++);for(k=2,10^m,d=digits(k);s=sum(i=1,#d,d[i]^n);if(s==k,return(k)));0

%o n=1;while(n<10,print1(a(n),", ");n++) \\ _Derek Orr_, Dec 19 2014

%Y Cf. A001694, A007532, A005934, A005188, A014576, A023052, A046074, A046761.

%Y In other bases: A033835 (base 3), A033836 (base 4), A033837 (base 5), A033838 (base 6), A033839 (base 7), A033840 (base 8), A033841 (base 9).

%K nonn,base,nice

%O 1,1

%A _N. J. A. Sloane_

%E Additional comments from _Lekraj Beedassy_, May 23 2001

%E Extended and cross-references edited by _Joseph Myers_, Jun 28 2009