A193567 Unhappy numbers which enter the cycle (4, 16, 37, 58, 89, 145, 42, 20) at 37.

3, 9, 18, 30, 33, 37, 39, 47, 56, 57, 59, 61, 65, 74, 75, 81, 90, 93, 95, 106, 108, 111, 114, 122, 125, 137, 138, 141, 144, 148, 152, 157, 158, 160, 173, 175, 178, 180, 183, 184, 185, 187, 212, 215, 221, 225, 227, 246, 251, 252, 256, 258, 264, 265, 272, 285

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Eric Weisstein's World of Mathematics, Unhappy Number.

Example

568 is such a number of height 7 because it enters the cycle at 37 in 7 steps: 568 -> 125 -> 30 -> 9 -> 81 -> 65 -> 61 -> 37 -> 58 -> 89 -> 145 -> 42 -> 20 -> 4 -> 16 -> 37 -> ...

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=37 then a:=[op(a), i] fi; od: print(op(a));

Crossrefs

Cf. A031177, A039943.

Sequence in context: A159794 A352643 A100967 * A045943 A134479 A184969

Adjacent sequences: A193564 A193565 A193566 * A193568 A193569 A193570

Keyword

nonn,base

Author

Martin Renner, Jul 31 2011

Status

approved