A274206 a(n) = the last nonzero digit of n followed by all the trailing zeros of n.

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

Offset: 1

Author

A. D. Skovgaard, Jun 13 2016

Keywords

• base
• easy
• nonn

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A010879, A037124 (these increasing distinct terms), A006519 (binary equivalent shown in decimal), A160094.

Programs

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 *)

PARI

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

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)/(1-x^10) + 10 g(x^10). (End)