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 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, 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 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A007953, A181190. Sequence in context: A112025 A060512 A060513 * A051713 A060225 A124901 Adjacent sequences:  A283528 A283529 A283530 * A283532 A283533 A283534 KEYWORD nonn,base,easy AUTHOR Paolo P. Lava, Mar 10 2017 STATUS approved

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Last modified January 28 10:02 EST 2020. Contains 331319 sequences. (Running on oeis4.)