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)

2, 0, 153, 1634, 4150, 548834, 1741725, 24678050, 146511208, 4679307774, 32164049650, 0, 564240140138, 28116440335967, 0, 4338281769391370, 233411150132317, 0, 1517841543307505039, 63105425988599693916

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

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.

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

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: A357542 A374275 A339185 * A012333 A012329 A064156

Adjacent sequences: A003318 A003319 A003320 * A003322 A003323 A003324

Keyword

nonn,base,nice

Author

N. J. A. Sloane

Extensions

Additional comments from Lekraj Beedassy, May 23 2001

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

Status

approved