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A003321
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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)
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31
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2, 0, 153, 1634, 4150, 548834, 1741725, 24678050, 146511208, 4679307774, 32164049650, 0, 564240140138, 28116440335967, 0, 4338281769391370, 233411150132317, 0, 1517841543307505039, 63105425988599693916
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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).
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LINKS
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Joseph Myers, Table of n, a(n) for n=1..109
L. E. Deimel, Narcissistic Numbers
H. Heinz, Narcissistic Numbers
Eric Weisstein's World of Mathematics, Narcissistic Number.
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A001694, A007532, A005934, A005188, A014576, A023052, A046074, A046761.
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: A181373 A046065 A339185 * A012333 A012329 A064156
Adjacent sequences: A003318 A003319 A003320 * A003322 A003323 A003324
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KEYWORD
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nonn,base,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Additional comments from Lekraj Beedassy, May 23 2001
Extended and cross-references edited by Joseph Myers, Jun 28 2009
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STATUS
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approved
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