A390774 Numbers whose final digit is at most 3.

0, 1, 2, 3, 10, 11, 12, 13, 20, 21, 22, 23, 30, 31, 32, 33, 40, 41, 42, 43, 50, 51, 52, 53, 60, 61, 62, 63, 70, 71, 72, 73, 80, 81, 82, 83, 90, 91, 92, 93, 100, 101, 102, 103, 110, 111, 112, 113, 120, 121, 122, 123, 130, 131, 132, 133, 140, 141, 142, 143, 150

Offset

0,3

Comments

A horse which is n inches high is described as a(n)/10 hands high: whole hands of 4 inches and the "decimal" point in a(n)/10 separating whole hands from remaining inches.

Links

Zhuorui He, Table of n, a(n) for n = 0..10000

Wikipedia, Hand (unit).

Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Formula

a(n) = 10 * floor(n/4) + (n mod 4). - Amiram Eldar, Nov 18 2025

From Stefano Spezia, Nov 26 2025: (Start)

G.f.: x*(1 + x + x^2 + 7*x^3)/((1 - x)^2*(1 + x)*(1 + x^2)).

E.g.f.: ((5*x - 3)*cosh(x) + 3*(cos(x) + sin(x)) + (5*x - 6)*sinh(x))/2. (End)

Example

A horse n=58 inches high is 14.2 hands so a(58) = 142.

Mathematica

a[n_] := Total[QuotientRemainder[n, 4] * {10, 1}]; Array[a, 61, 0] (* Amiram Eldar, Nov 18 2025 *)

Prog

(Python)
def A390774(n): return (lambda x:x[0]*10+x[1])(divmod(n, 4)) # Chai Wah Wu, Nov 25 2025

Crossrefs

Cf. A008592 (final digit at most 0), A197652 (at most 1), A391163 (at most 2), A293292 (at most 4), A391164 (at most 5), A272576 (at most 7), A001477 (at most 9).

Sequence in context: A362089 A301382 A288657 * A055655 A371030 A276326

Adjacent sequences: A390771 A390772 A390773 * A390775 A390776 A390777

Keyword

nonn,easy,base

Author

J. Lowell, Nov 18 2025

Status

approved