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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.)