OFFSET
0,11
COMMENTS
Alternative definition: number of steps to return to n under a transform where the MSD(n) is deleted and as LSD(n) is concatenated Sd(n) mod 10, where Sd(n) is the sum of the digits of n.
Numbers n that need exactly n steps are 1, 20, 124, 1560.
Number of steps to return to 10^k, with k = 0, 1, 2, ..., are listed in A181190.
LINKS
Paolo P. Lava, Table of n, a(n) for n = 0..10000
EXAMPLE
a(18) = 12 because:
(1 + 8) mod 10 = 9 -> 89;
(8 + 9) mod 10 = 7 -> 97;
(9 + 7) mod 10 = 6 -> 76;
(7 + 6) mod 10 = 3 -> 63;
(6 + 3) mod 10 = 9 -> 39;
(3 + 9) mod 10 = 2 -> 92;
(9 + 2) mod 10 = 1 -> 21;
(2 + 1) mod 10 = 3 -> 13;
(1 + 3) mod 10 = 4 -> 34;
(3 + 4) mod 10 = 7 -> 47;
(4 + 7) mod 10 = 1 -> 71;
(7 + 1) mod 10 = 8 -> 18;
a(68) = 4 because:
(6 + 8) mod 10 = 4 -> 84;
(8 + 4) mod 10 = 2 -> 42;
(4 + 2) mod 10 = 6 -> 26;
(2 + 6) mod 10 = 8 -> 68.
MAPLE
S:=proc(w) local x, y, z; x:=w; y:=0; for z from 1 to ilog10(x)+1 do y:=y+(x mod 10); x:=trunc(x/10); od; y mod 10; end: P:=proc(q) local a, k, n; for n from 0 to q do a:=n;
for k from 1 to q do a:=10*(a mod 10^(ilog10(n)))+S(a); if a=n then print(k);
break; fi; od; od; end: P(10^5);
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Paolo P. Lava, Mar 10 2017
STATUS
approved