A283531 Number of steps to return to n through a chain-addition sequence mod 10 with window of size equal to the number of digits of n.
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 60, 60, 60, 12, 60, 60, 60, 60, 12, 60, 20, 12, 20, 60, 20, 60, 4, 60, 20, 60, 60, 60, 60, 60, 12, 60, 60, 60, 60, 12, 20, 60, 4, 60, 20, 60, 20, 12, 20, 60, 3, 60, 60, 60, 60, 3, 60, 60, 60, 60, 20, 60, 20, 12, 20, 60, 20, 60, 4, 60
Offset: 0
Examples
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.
Links
- Paolo P. Lava, Table of n, a(n) for n = 0..10000
Programs
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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);
Comments