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 A222259 Lexicographically earliest injective sequence of positive integers such that the sum of 8 consecutive terms is always divisible by 8. 2

%I #10 Jan 02 2023 12:30:49

%S 1,2,3,4,5,6,7,12,9,10,11,20,13,14,15,28,17,18,19,36,21,22,23,44,25,

%T 26,27,52,29,30,31,60,33,34,35,68,37,38,39,76,41,42,43,84,45,46,47,92,

%U 49,50,51,100,53,54,55,108,57,58,59,116,61,62,63,124,65,66,67,132,69,70,71,140,73,74,75,148,77,78,79,156,81,82,83,164,85,86,87,172,89,90

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

%H E. Angelini, <a href="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

%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 + x^6 + 4*x^7)/((1 - x)*(1 + x)*(1 + x^2))^2.

%F a(n)=n unless n=0 (mod 4) in which case a(n)=2n-4.

%Y Cf. A222256, A222257, A222258, A222260, A222261.

%K nonn

%O 1,2

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

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Last modified September 8 17:49 EDT 2024. Contains 375753 sequences. (Running on oeis4.)