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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.

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

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..90.

E. Angelini, k-chunks sum and division by k, post to the SeqFan list, Mar 22 2013

FORMULA

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

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.

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

CROSSREFS

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