A014576 Smallest n-digit narcissistic (or Armstrong) number: smallest n-digit number equal to sum of n-th powers of its digits (or 0 if no such number exists).

1, 0, 153, 1634, 54748, 548834, 1741725, 24678050, 146511208, 4679307774, 32164049650, 0, 0, 28116440335967, 0, 4338281769391370, 21897142587612075, 0, 1517841543307505039, 63105425988599693916, 128468643043731391252, 0

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• fini
• full
• nice

References

• M. Gardner, The Magic Numbers of Dr Matrix. Prometheus, Buffalo, NY, 1985, p. 249.
• C. A. Pickover, Keys to Infinity. New York: W. H. Freeman, pp. 169-170, 1995.

Links

• T. D. Noe, Table of n, a(n) for n=1..39 (complete sequence)
• Harvey Heinz, Narcissistic Numbers
• Mike Keith, Wild Narcissistic Numbers (Copy as of May 2008 on web.archive.org - page does not exist any more.)
• Eric Weisstein's World of Mathematics, Narcissistic Number.

Crossrefs

Cf. A001694, A007532, A005934, A005188, A003321, A023052, A046074.

Programs

Mathematica

(* This program is not suitable for more than 10 terms *) a[n_] := For[k = 10^(n-1), True, k++, If[k > 10^n - 1, Return[0], If[k == Total[ IntegerDigits[k]^IntegerLength[k] ], Return[k] ] ] ]; Table[ Print[an = a[n]]; an, {n, 1, 10}] (* Jean-François Alcover, Oct 15 2013 *)

Extensions

Terms and links added by Patrick De Geest, Oct 1998

Broken links fixed by M. F. Hasler, Feb 12 2013