%I A005188 M0488
%S A005188 1,2,3,4,5,6,7,8,9,153,370,371,407,1634,8208,9474,54748,92727,93084,
%T A005188 548834,1741725,4210818,9800817,9926315,24678050,24678051,88593477,
%U A005188 146511208,472335975,534494836,912985153,4679307774,32164049650,32164049651
%N A005188 Armstrong (or Plus Perfect, or narcissistic) numbers: n-digit numbers 
               equal to sum of n-th powers of their digits (a finite sequence, the 
               last term being 115132219018763992565095597973971522401).
%C A005188 Let n = d_1 d_2 ... d_k in base 10; then n = Sum_{i=1..k} d_i^k.
%C A005188 These are the fixed points in the "Recurring Digital Invariant Variant" 
               described in A151543.
%D A005188 J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 88, pp 30-31, 
               Ellipses, Paris 2008.
%D A005188 Lionel E. Deimel, Jr. and Michael T. Jones, Finding Pluperfect Digital 
               Invariants: Techniques, Results and Observations, J. Rec. Math., 
               14 (1981), 87-108.
%D A005188 J. P. Lamoitier, Fifty Basic Exercises. SYBEX Inc., 1981.
%D A005188 Tomas Antonio Mendes Oliveira e Silva (tos(AT)ci.ua.pt) gave the full 
               sequence in a posting (Article 42889) to sci.math on May 09 1994.
%D A005188 Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 
               68.
%D A005188 Joe Roberts, "The Lure of the Integers", page 35.
%D A005188 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A005188 T. D. Noe, <a href="b005188.txt">Table of n, a(n) for n=1..88</a> (the 
               full list of terms, from Winter)
%H A005188 Anonymous, <a href="http://everything2.net/index.pl?node_id=1525466&displaytype=printable&lastnode_id=1525466\
               ">Narcissistic number</a>
%H A005188 L. E. Deimel, <a href="http://www.deimel.org/rec_math/DI_1.htm">Narcissistic 
               Numbers</a>
%H A005188 H. Heinz, <a href="http://www.geocities.com/CapeCanaveral/Launchpad/4057/
               narciss.htm#PDIs">Narcissistic Numbers</a>
%H A005188 W. Lopez, PlanetMath.Org, <a href="http://planetmath.org/encyclopedia/
               ArmstrongNumber.html">Armstrong number</a>
%H A005188 W. Schneider, <a href="http://web.archive.org/web/2004/www.wschnei.de/
               digit-related-numbers/pdi.html">Perfect Digital Invariants: Pluperfect 
               Digital Invariants(PPDIs)</a>
%H A005188 B. Shader, <a href="http://everything2.net/index.pl?node_id=1407017&displaytype=printable&lastnode_id=1407017\
               ">Armstrong number</a>
%H A005188 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ArmstrongNumber.html">Link to a section of The World of Mathematics 
               (1).</a>
%H A005188 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               NarcissisticNumber.html">Link to a section of The World of Mathematics 
               (2).</a>
%H A005188 Wikipedia, <a href="http://en.wikipedia.org/wiki/Armstrong_number">Narcissistic 
               number</a>
%H A005188 D. T. Winter, <a href="http://ftp.cwi.nl/dik/Armstrong">Table of Armstrong 
               Numbers</a>
%e A005188 153 = 1^3 + 5^3 + 3^3, 4210818 = 4^7 + 2^7 + 1^7 + 0^7 + 8^7 + 1^7 + 
               8^7.
%t A005188 f[n_] := Plus @@ (IntegerDigits[n]^Floor[ Log[10, n] + 1]); Select[ Range[10^7], 
               f[ # ] == # &] (from Robert G. Wilson v (rgwv(AT)rgwv.com), May 04 
               2005)
%Y A005188 Cf. A001694, A007532, A005934, A003321, A014576, A046074.
%Y A005188 Similar to but different from A023052.
%Y A005188 Cf. A151543.
%Y A005188 Cf. A010343 to A010354 (bases 4 to 9). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 28 2009]
%Y A005188 Sequence in context: A151544 A032561 A023052 this_sequence A032569 A039723 
               A002998
%Y A005188 Adjacent sequences: A005185 A005186 A005187 this_sequence A005189 A005190 
               A005191
%K A005188 nonn,base,fini,nice
%O A005188 1,2
%A A005188 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A005188 32164049651 from Amit Munje (amit.munje(AT)gmail.com), Oct 07 2006