A193567 Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 37.

3, 9, 18, 30, 33, 37, 39, 47, 56, 57, 59, 61, 65, 74, 75, 81, 90, 93, 95, 106, 108, 111, 114, 122, 125, 137, 138, 141, 144, 148, 152, 157, 158, 160, 173, 175, 178, 180, 183, 184, 185, 187, 212, 215, 221, 225, 227, 246, 251, 252, 256, 258, 264, 265, 272, 285

Offset: 1

Author

Martin Renner, Jul 31 2011

Keywords

• nonn
• base

Examples

			568 is such a number of height 7 because it enters the cycle at 37 in 7 steps: 568 -> 125 -> 30 -> 9 -> 81 -> 65 -> 61 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> ...
		

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=37 then a:=[op(a),i] fi; od: print(op(a));