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

5, 6, 8, 12, 14, 17, 21, 22, 25, 27, 29, 34, 35, 36, 41, 43, 45, 46, 48, 50, 52, 53, 54, 55, 60, 63, 64, 66, 67, 71, 72, 76, 80, 84, 85, 89, 92, 99, 102, 104, 107, 112, 115, 118, 120, 121, 123, 124, 126, 127, 132, 135, 136, 140, 142, 146, 147, 151

Offset: 1

Author

Martin Renner, Jul 31 2011

Keywords

• nonn
• base

Examples

			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 -> ...
		

Links

• Eric Weisstein's World of Mathematics, Unhappy Number.

Crossrefs

Cf. A031177, A039943.

Programs

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=89 then a:=[op(a),i] fi; od: print(op(a));