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

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.

Sequence in context: A358254 A175500 A356253 * A243575 A284447 A032985

Adjacent sequences: A222256 A222257 A222258 * A222260 A222261 A222262

Keyword

nonn

Author

Eric Angelini and M. F. Hasler, Mar 23 2013

Status

approved