A222258 - OEIS

%I #14 Dec 23 2024 14:53:43

%S 0,1,2,3,4,5,6,11,8,9,10,19,12,13,14,27,16,17,18,35,20,21,22,43,24,25,

%T 26,51,28,29,30,59,32,33,34,67,36,37,38,75,40,41,42,83,44,45,46,91,48,

%U 49,50,99,52,53,54,107,56,57,58,115,60,61,62,123,64,65,66,131,68,69,70,139,72,73,74,147,76,77,78,155,80,81,82,163,84,85,86,171,88,89

%N Lexicographically earliest injective sequence of nonnegative integers such that the sum of 8 consecutive terms is always divisible by 8.

%H E. Angelini, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2013-March/010956.html">k-chunks sum and division by k</a>, post to the SeqFan list, Mar 22 2013

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).

%F a(n) = 2 a(n-4) - a(n-8).

%F G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 3*x^4 + 2*x^5 + 5*x^6)/((1 - x)*(1 + x)*(1 + x^2))^2.

%F a(n)=n unless n=3 (mod 4) in which case a(n)=2n-3.

%o (PARI) A222258(n)=if(n%4==3,n*2-3,n)

%Y Cf. A222256, A222257, A222259, A222260, A222261.

%K nonn

%O 0,3

%A _Eric Angelini_ and _M. F. Hasler_, Mar 23 2013