A193566 - OEIS

%I #21 Feb 11 2024 23:45:06

%S 15,16,26,40,51,62,69,88,96,105,117,128,134,143,150,155,156,165,171,

%T 182,206,218,237,247,260,273,274,278,279,281,287,297,314,327,341,372,

%U 399,400,413,427,431,448,458,466,472,484,485,501,510,515,516,548,551

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnhappyNumber.html">Unhappy Number</a>.

%e 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 -> ...

%p 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:

%p 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));

%Y Cf. A031177, A039943.

%K nonn,base

%O 1,1

%A _Martin Renner_, Jul 31 2011