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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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30
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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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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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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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KEYWORD
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nonn,base,nice
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AUTHOR
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EXTENSIONS
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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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