A118740 Let L_n be the infinite sequence formed by starting with 1 and repeatedly placing the first digit at the end of the number and adding n to get the next term. Sequence gives number of steps for L_n to enter a cycle, or -1 if no cycle is ever reached.

1, 6, 1, 4, 3, 3, 16, 3, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 24, 6, 13, 21, 6, 35, 9, 2, 25, 1, 6, 1, 5, 1, 1, 1, 2, 22, 3, 1, 52, 5, 1, 16, 21, 2, 19, 10, 11, 18, 32, 9, 12, 1, 2, 1, 3, 2, 3, 55, 9, 4, 18, 2, 3, 2, 2, 1, 3, 8, 58, 1, 2, 3, 3, 3, 2, 2, 3, 81, 35, 2, 3, 2, 2, 13, 2, 2, 3, 4, 2, 3, 3, 2, 19, 2, 2

Offset

1,2

Comments

It is conjectured that L_n always reaches a cycle.

From Robert Israel, Dec 25 2017: (Start)

a(10^k-1) = 1 for k >= 1.

a(19*10^k-1) = 2.

Empirical:

a(10^k) = k+1 for all k.

a(2*10^k) = 9*k+15 for k >= 1.

a(2*10^k-1) = 1 for k >= 1.

a(10^k+1) = k for k >= 1.

a(2*10^k+1) = 3*k+3 for k >= 1. (End)

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

L_2 = [1,3,5,7,9,11,13,33,35,55,57,77,79,99,101,13,...] enters a cycle of length 9 after 6 steps.

Maple

f:= proc(n) local t, k, S, d;
    t:= 1; S[t]:= 0;
    for k from 1 do
      d:= 10^ilog10(t);
      t:= 10*(t mod d)+ floor(t/d) + n;
      if assigned(S[t]) then return S[t] fi;
      S[t]:= k;
    od
end proc:
map(f, [$1..100]); # Robert Israel, Dec 25 2017

Crossrefs

Cf. A118739.

Sequence in context: A144540 A292107 A212037 * A301431 A200302 A082344

Adjacent sequences: A118737 A118738 A118739 * A118741 A118742 A118743

Keyword

base,nonn

Author

Luc Stevens (lms022(AT)yahoo.com), May 24 2006

Extensions

Corrected by Robert Israel, Dec 25 2017

Status

approved