

A283531


Number of steps to return to n through a chainaddition 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
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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



