A193572 Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 20.
20, 24, 204, 224, 240, 242, 402, 420, 422, 1133, 1313, 1331, 2004, 2024, 2040, 2042, 2204, 2240, 2400, 2402, 2420, 3113, 3131, 3311, 4002, 4020, 4022, 4200, 4202, 4220, 4899, 4989, 4998, 5779, 5797, 5977, 7579, 7597, 7759, 7795, 7957, 7975, 8499, 8949, 8994
Offset: 1
Examples
4899 is such a number of height 3 because it enters the cycle at 20 in 3 steps: 4899 -> 242 -> 24 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> ...
Links
- Eric Weisstein's World of Mathematics, Unhappy Number.
Programs
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Maple
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: a:=[]: for i from 1 while nops(a)<30 do Q:=S(i); A:=Q[nops(Q)]; if A=20 then a:=[op(a),i] fi; od: print(op(a));