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

1,2

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)/(1-x^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: A053831 A263131 A349315 * A214949 A067453 A203814

Adjacent sequences: A274203 A274204 A274205 * A274207 A274208 A274209

Keyword

base,easy,nonn

Author

A. D. Skovgaard, Jun 13 2016

Status

approved