A193571 Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 42.

42, 154, 389, 398, 415, 451, 514, 541, 839, 893, 938, 983, 1045, 1054, 1126, 1162, 1216, 1261, 1344, 1405, 1434, 1443, 1450, 1504, 1540, 1588, 1612, 1621, 1669, 1696, 1858, 1885, 1966, 2116, 2161, 2235, 2253, 2325, 2352, 2523, 2532, 2611, 3089, 3098, 3144

Offset: 1

Author

Martin Renner, Jul 31 2011

Keywords

• nonn
• base

Examples

			389 is such a number of height 2 because it enters the cycle at 42 in 2 steps: 389 -> 154 -> 42 -> 20 -> 4 -> 16 -> 37 -> 58 -> 89 -> 145 -> 42 -> ...
		

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=42 then a:=[op(a),i] fi; od: print(op(a));