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A193569 Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 89. 0

%I #20 Feb 11 2024 22:30:07

%S 5,6,8,12,14,17,21,22,25,27,29,34,35,36,41,43,45,46,48,50,52,53,54,55,

%T 60,63,64,66,67,71,72,76,80,84,85,89,92,99,102,104,107,112,115,118,

%U 120,121,123,124,126,127,132,135,136,140,142,146,147,151

%N Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 89.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnhappyNumber.html">Unhappy Number</a>.

%e 15999 is such a number of height 12 because it enters the cycle at 89 in 12 steps: 15999 -> 269 -> 121 -> 6 -> 36 -> 45 -> 41 -> 17 -> 50 -> 25 -> 29 -> 85 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89 -> ...

%p S:=proc(n) local Q,k,N,z; Q:=[n]; for k from 1 do N:=convert(Q[k],base,10); z:=sum(N['i']^2,'i'=1..nops(N)); if not member(z,Q) then Q:=[op(Q),z]; else Q:=[op(Q),z]; break; fi; od; return Q; end:

%p a:=[]: for i from 1 while nops(a)<30 do Q:=S(i); A:=Q[nops(Q)]; if A=89 then a:=[op(a),i] fi; od: print(op(a));

%Y Cf. A031177, A039943.

%K nonn,base

%O 1,1

%A _Martin Renner_, Jul 31 2011

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