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

1,1

Links

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

Eric Weisstein's World of Mathematics, Unhappy Number.

Example

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 -> ...

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));

Crossrefs

Cf. A031177, A039943.

Sequence in context: A342941 A377160 A046417 * A079832 A037971 A022105

Adjacent sequences: A193563 A193564 A193565 * A193567 A193568 A193569

Keyword

nonn,base

Author

Martin Renner, Jul 31 2011

Status

approved