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A034326 Hours struck by a clock. 6

%I #45 Jan 27 2024 18:40:29

%S 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,

%T 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,

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

%N Hours struck by a clock.

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

%H Gordon Hamilton and others, <a href="/A034326/a034326.pdf">Integer Sequences K-12 (Banff 2015)</a>.

%H Gordon Hamilton and others, <a href="/A034326/a034326_1.pdf">Additional Notes on Sequences Considered at Banff Conference</a>.

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,1).

%F From _Wesley Ivan Hurt_, Sep 23 2014: (Start)

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

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

%F 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)

%F From _M. F. Hasler_, Sep 25 2014: (Start)

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

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

%F a(n) = n - 12*floor((n-1)/12). - _Mikael Aaltonen_, Jan 03 2014

%p A034326:=n->((n-1) mod 12)+1: seq(A034326(n), n=1..100); # _Wesley Ivan Hurt_, Sep 23 2014

%t Table[Mod[n - 1, 12] + 1, {n, 100}] (* _Wesley Ivan Hurt_, Sep 23 2014 *)

%t PadRight[{},120,Range[12]] (* _Harvey P. Dale_, Aug 30 2020 *)

%o (PARI) A034326(n) = (n-1)%12 + 1 \\ _Michael B. Porter_, Feb 02 2010

%o (Haskell) A034326 n = succ (pred n `mod` 12) -- _Walt Rorie-Baety_, May 18 2012

%Y Cf. A010881 (n mod 12).

%K nonn,easy

%O 1,2

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

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)