

A274206


a(n) = the last nonzero digit of n followed by all the trailing zeros of n.


1



1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 1, 2, 3, 4, 5, 6, 7, 8, 9, 30, 1, 2, 3, 4, 5, 6, 7, 8, 9, 40, 1, 2, 3, 4, 5, 6, 7, 8, 9, 50, 1, 2, 3, 4, 5, 6, 7, 8, 9, 60, 1, 2, 3, 4, 5, 6, 7, 8, 9, 70, 1, 2, 3, 4, 5, 6, 7, 8, 9, 80
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OFFSET

1,2


COMMENTS

a(n) is the number formed by the rightmost A160094(n) digits  only the position(s) that changed  of a decimal counter (e.g., an odometer) after it increments from n  1 to n.  Rick L. Shepherd, Jun 29 2016


LINKS

A. D. Skovgaard, Table of n, a(n) for n = 1..10000


FORMULA

a(n) = n mod 10 if n is not a multiple of 10.
From Robert Israel, Aug 08 2016: (Start)
a(10*n) = 10*a(n).
a(10*n+k) = k for 1 <= k <= 9.
G.f. g(x) satisfies g(x) = (x+2x^2+...+9x^9)/(1x^10) + 10 g(x^10). (End)


EXAMPLE

a(1) = 1 because when 1 is added to 1  1 = 0, the units digit changes so the units digit of 1 is shown.
a(110) = 10 because when 1 is added to 109, the tens digit and the units digit change, so the last two digits of 110 are shown.
a(1000) = 1000 because when 1 is added to 999, all the digits change so they are all shown.


MAPLE

f:= n > n mod 10^(1+min(padic:ordp(n, 2), padic:ordp(n, 5))):
map(f, [$1..100]); # Robert Israel, Aug 08 2016


MATHEMATICA

Table[FromDigits@ Join[{Last@ #}, Table[0, {Log10[n/FromDigits@ #]}]] &@ Select[IntegerDigits@ n, # != 0 &], {n, 120}] (* Michael De Vlieger, Jun 29 2016 *)


PROG

(PARI) a(n) = n%10^(valuation(n, 10)+1); \\ David A. Corneth, Jun 29 2016


CROSSREFS

Cf. A010879, A037124 (these increasing distinct terms), A006519 (binary equivalent shown in decimal), A160094.
Sequence in context: A010889 A053831 A263131 * A214949 A067453 A203814
Adjacent sequences: A274203 A274204 A274205 * A274207 A274208 A274209


KEYWORD

base,easy,nonn


AUTHOR

A. D. Skovgaard, Jun 13 2016


STATUS

approved



