A034326 Hours struck by a clock.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 8, 9

Offset: 1

Author

Tae Su Chung (cts32(AT)hanmail.net)

Keywords

• nonn
• easy

Comments

Period 12: repeat [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12].

Links

• Gordon Hamilton and others, Integer Sequences K-12 (Banff 2015).
• Gordon Hamilton and others, Additional Notes on Sequences Considered at Banff Conference.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A010881 (n mod 12).

Programs

Haskell

A034326 n = succ (pred n `mod` 12) -- Walt Rorie-Baety, May 18 2012

Maple

A034326:=n->((n-1) mod 12)+1: seq(A034326(n), n=1..100); # Wesley Ivan Hurt, Sep 23 2014

Mathematica

Table[Mod[n - 1, 12] + 1, {n, 100}] (* Wesley Ivan Hurt, Sep 23 2014 *)
PadRight[{},120,Range[12]] (* Harvey P. Dale, Aug 30 2020 *)

PARI

A034326(n) = (n-1)%12 + 1 \\ Michael B. Porter, Feb 02 2010

Formula

From Wesley Ivan Hurt, Sep 23 2014: (Start)

a(n) = (n-1) mod 12 + 1.

a(n) = a(n-12), n > 12.

G.f.: 11 + 1/(1-x) + x * (x + 2*x^2 + 3*x^3 + 4*x^4 + 5*x^5 + 6*x^6 + 7*x^7 + 8*x^8 + 9*x^9 + 10*x^10 + 11*x^11) / (1-x^12). (End)

From M. F. Hasler, Sep 25 2014: (Start)

a(n) = A010881(n-1) + 1.

G.f.: Sum_{k=1..12} k*x^k/(1-x^12). (End)

a(n) = n - 12*floor((n-1)/12). - Mikael Aaltonen, Jan 03 2014