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

1,1

Links

Table of n, a(n) for n=1..53.

Eric Weisstein's World of Mathematics, Unhappy Number.

Example

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 -> ...

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));

Crossrefs

Cf. A031177, A039943.

Sequence in context: A182100 A327484 A006894 * A198864 A038093 A057284

Adjacent sequences: A193562 A193563 A193564 * A193566 A193567 A193568

Keyword

nonn,base

Author

Martin Renner, Jul 31 2011

Status

approved