%I A039943
%S A039943 0,1,4,16,20,37,42,58,89,145
%N A039943 Every integer eventually goes to one of these under the x goes to sum 
               of squares of digits map.
%C A039943 The subset of the first three terms would also satisfy the current definition. 
               An alternate definition would be: Periodic points of A003132. [From 
               M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
%D A039943 A. Porges, A set of eight numbers, Amer. Math. Monthly, 52 (1945), 379-382.
%H A039943 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               HappyNumber.html">Happy Number</a>
%H A039943 Wikipedia, <a href="http://en.wikipedia.org/wiki/Periodic_point">Periodic 
               point</a>. [From M. F. Hasler (MHasler(AT)univ-ag.fr), May 24 2009]
%t A039943 lst = {}; Do[a = NestWhile[Plus @@ (IntegerDigits@#^2) &, n, Unequal, 
               All]; If[FreeQ[lst, a], AppendTo[lst, a]], {n, 10^4}] (from Robert 
               G. Wilson v (rgwv(at)rgwv.com), Jan 19 2006)
%Y A039943 Cf. A000216, A003621.
%Y A039943 Cf. A003132 (the iterated map), A003621, A039943, A031176, A007770, A000216 
               (orbit of 2), A000218 (orbit of 3), A080709 (orbit of 4, the only 
               nontrivial limit cycle), A000221 (orbit of 5), A008460 (orbit of 
               6), A008462 (orbit of 8), A008463 (orbit of 9), A139566 (orbit of 
               15), A122065 (orbit of 74169). [From M. F. Hasler (MHasler(AT)univ-ag.fr), 
               May 24 2009]
%Y A039943 Sequence in context: A146510 A032827 A071966 this_sequence A067671 A075331 
               A065661
%Y A039943 Adjacent sequences: A039940 A039941 A039942 this_sequence A039944 A039945 
               A039946
%K A039943 nonn,fini,full,base
%O A039943 0,3
%A A039943 N. J. A. Sloane (njas(AT)research.att.com).