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A003321 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.
(Formerly M5403)
30
2, 0, 153, 1634, 4150, 548834, 1741725, 24678050, 146511208, 4679307774, 32164049650, 0, 564240140138, 28116440335967, 0, 4338281769391370, 233411150132317, 0, 1517841543307505039, 63105425988599693916 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Except for the initial term, this is the third column of A252648. - M. F. Hasler, Feb 16 2015
a(n) = 0 if n>1 and in A262094. - Dmitry Kamenetsky, Jun 05 2020
REFERENCES
M. Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 249.
J. S. Madachy, Mathematics on Vacation, Thomas Nelson and Sons Ltd. 1966, p. 164.
J. S. Madachy, Madachy's Mathematical Recreations, Dover, p. 164.
C. A. Pickover, Keys to Infinity. New York: W. H. Freeman, pp. 169-170, 1995.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
L. E. Deimel, Narcissistic Numbers
Eric Weisstein's World of Mathematics, Narcissistic Number.
EXAMPLE
1^3 + 5^3 + 3^3 = 153.
1*0^17 + 5*1^17 + 2*2^17 + 4*3^17 + 1*4^17 + 1*5^17 + 1*7^17 = 233411150132317.
PROG
(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
n=1; while(n<10, print1(a(n), ", "); n++) \\ Derek Orr, Dec 19 2014
CROSSREFS
In other bases: A033835 (base 3), A033836 (base 4), A033837 (base 5), A033838 (base 6), A033839 (base 7), A033840 (base 8), A033841 (base 9).
Sequence in context: A046065 A357542 A339185 * A012333 A012329 A064156
KEYWORD
nonn,base,nice
AUTHOR
EXTENSIONS
Additional comments from Lekraj Beedassy, May 23 2001
Extended and cross-references edited by Joseph Myers, Jun 28 2009
STATUS
approved

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Last modified March 19 04:58 EDT 2024. Contains 370952 sequences. (Running on oeis4.)