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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.
(Formerly M5403)
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)



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).


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.


2*2^17+4*3^17+4^17+5+5^17+7^17 = 233411150132317.


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: A033838 A181373 A046065 * A012333 A012329 A064156

Adjacent sequences:  A003318 A003319 A003320 * A003322 A003323 A003324




N. J. A. Sloane.


Additional comments from Lekraj Beedassy, May 23 2001

Extended and cross-references edited by Joseph Myers, Jun 28 2009



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Last modified December 22 07:03 EST 2014. Contains 252328 sequences.