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

1,1

Links

Table of n, a(n) for n=1..45.

Eric Weisstein's World of Mathematics, Unhappy Number.

Example

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 -> ...

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));

Crossrefs

Cf. A031177, A039943.

Sequence in context: A189500 A350579 A075289 * A326384 A263285 A263300

Adjacent sequences: A193568 A193569 A193570 * A193572 A193573 A193574

Keyword

nonn,base

Author

Martin Renner, Jul 31 2011

Status

approved