A193565 Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 4.

2, 4, 11, 78, 87, 101, 110, 113, 131, 168, 179, 186, 197, 200, 249, 257, 259, 275, 294, 295, 311, 429, 449, 467, 476, 492, 494, 527, 529, 559, 567, 572, 576, 592, 595, 618, 647, 657, 674, 675, 681, 708, 719, 725, 746, 752, 756, 764, 765, 779, 780, 791, 797

Offset: 1

Author

Martin Renner, Jul 31 2011

Keywords

• nonn
• base

Examples

			7899 is such a number of height 6 because it enters the cycle at 4 in 6 steps: 7899 -> 275 -> 78 -> 113 -> 11 -> 2 -> 4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> ...
		

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=4 then a:=[op(a),i] fi; od: print(op(a));