A193566 Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 16.

15, 16, 26, 40, 51, 62, 69, 88, 96, 105, 117, 128, 134, 143, 150, 155, 156, 165, 171, 182, 206, 218, 237, 247, 260, 273, 274, 278, 279, 281, 287, 297, 314, 327, 341, 372, 399, 400, 413, 427, 431, 448, 458, 466, 472, 484, 485, 501, 510, 515, 516, 548, 551

Offset: 1

Author

Martin Renner, Jul 31 2011

Keywords

• nonn
• base

Examples

			466 is such a number of height 8 because it enters the cycle at 16 in 8 steps: 466 -> 88 -> 128 -> 69 -> 117 -> 51 -> 26 -> 40 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> ...
		

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=16 then a:=[op(a),i] fi; od: print(op(a));