Search: id:A007770
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%I A007770
%S A007770 1,7,10,13,19,23,28,31,32,44,49,68,70,79,82,86,91,94,97,100,103,109,
%T A007770 129,130,133,139,167,176,188,190,192,193,203,208,219,226,230,236,
%U A007770 239,262,263,280,291,293,301,302,310,313,319,320,326,329,331,338
%N A007770 Happy numbers: numbers whose trajectory under iteration of sum of squares 
               of digits map includes 1.
%C A007770 Sometimes called friendly numbers, but this usage is deprecated.
%D A007770 R. K. Guy, Unsolved Problems Number Theory, Sect. E34.
%D A007770 E. El-Sedy and S. Siksek, On happy numbers, Rocky Mountain J. Math. 30 
               (2000), 565-570.
%D A007770 J. N. Kapur, Reflections of a Mathematician, Chap. 34 pp. 319-324, Arya 
               Book Depot New Delhi 1996.
%H A007770 Jud McCranie, <a href="b007770.txt">Table of n, a(n) for n = 1..143071</
               a>
%H A007770 Hao Pan, <a href="http://arXiv.org/abs/math.NT/0607213">Consecutive happy 
               numbers</a>
%H A007770 W. Schneider, <a href="http://www.wschnei.de/digit-related-numbers/happy-numbers.html">
               Happy Numbers</a> (Includes list of terms below 10000)
%H A007770 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Digitaddition.html">Link to a section of The World of Mathematics.</
               a>
%H A007770 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HappyNumber.html">Link to a section of The World of Mathematics.</
               a>
%H A007770 Wikipedia, <a href="http://en.wikipedia.org/wiki/Happy_number">Happy 
               number</a>
%H A007770 Doctor Who, <a href="http://www.youtube.com/watch?v=ee2If8jSxUo">Episode 
               42</a>
%H A007770 Wikipedia, <a href="http://en.wikipedia.org/wiki/42_(Doctor_Who)">Doctor 
               Who, Episode 42</a>
%e A007770 1 is OK. 2 --> 4 --> 16 --> 37 --> ... --> 4, which repeats with period 
               8, so never reaches 1, so 2 (and 4) are unhappy.
%e A007770 Someone suggested that 98 is happy, but it is not.
%Y A007770 Cf. A001273, A035497 (happy primes), A046519, A031177, A002025, A050972, 
               A050973, A074902.
%Y A007770 Cf. A035502, A068571, A072494.
%Y A007770 Sequence in context: A096678 A026319 A120153 this_sequence A114961 A123834 
               A064629
%Y A007770 Adjacent sequences: A007767 A007768 A007769 this_sequence A007771 A007772 
               A007773
%K A007770 nonn,base,nice,easy
%O A007770 1,2
%A A007770 N. J. A. Sloane (njas(AT)research.att.com), A.R.McKenzie(AT)bnr.co.uk
%E A007770 Doctor Who links from David Applegate, Oct 06 2008

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