A222259 - OEIS

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

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

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.

a(n) = A222258(n-1) + 1. - Paolo Xausa, Oct 02 2025