A391164 Numbers whose final digit is at most 5.

0, 1, 2, 3, 4, 5, 10, 11, 12, 13, 14, 15, 20, 21, 22, 23, 24, 25, 30, 31, 32, 33, 34, 35, 40, 41, 42, 43, 44, 45, 50, 51, 52, 53, 54, 55, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 80, 81, 82, 83, 84, 85, 90, 91, 92, 93, 94, 95, 100, 101, 102, 103, 104, 105

Offset

0,3

Comments

Numbers that are {0, 1, 2, 3, 4, 5} mod 10.

Union of A008592, A017281, A017293, A017305, A017317, and A017329.

Differs from A007092 for n >= 36. A007092(36) = 100, while a(36) = 60.

In cricket, balls bowled are measured in whole overs of 6 balls and a partial over of 0 to 5 balls.

Links

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

Wikipedia, Over (cricket).

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

Formula

a(n) = 10 * floor(n/6) + (n mod 6) = 10 * A152467(n) + A010875(n).

G.f.: x*(1 + x + x^2 + x^3 + x^4 + 5*x^5)/((-1 + x)^2*(1 + x)*(1 - x + x^2)*(1 + x + x^2)).

Example

Bowling 63 balls results in 10.3 overs, so a(63) = 103.

Mathematica

a[n_] := Total[QuotientRemainder[n, 6] * {10, 1}]; Array[a, 66, 0]

Crossrefs

Cf. A010875, A017281, A017293, A017305, A017317, A017329, A152467.

Cf. A008592 (at most 0), A197652 (at most 1), A391163 (at most 2), A390774 (at most 3), A293292 (at most 4), A272576 (at most 7), A001477 (trivial, at most 9).

Sequence in context: A072701 A261039 A266117 * A037473 A007092 A395817

Adjacent sequences: A391161 A391162 A391163 * A391165 A391166 A391167

Keyword

nonn,easy,base

Author

Jason Bard, Dec 01 2025

Status

approved