A222261 Lexicographically earliest injective sequence of positive integers such that the sum of 10 consecutive terms is always divisible by 10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 15, 11, 12, 13, 14, 25, 16, 17, 18, 19, 35, 21, 22, 23, 24, 45, 26, 27, 28, 29, 55, 31, 32, 33, 34, 65, 36, 37, 38, 39, 75, 41, 42, 43, 44, 85, 46, 47, 48, 49, 95, 51, 52, 53, 54, 105, 56, 57, 58, 59, 115, 61, 62, 63, 64, 125, 66, 67, 68, 69, 135, 71, 72, 73, 74, 145, 76, 77, 78, 79, 155, 81

Offset

1,2

Links

Table of n, a(n) for n=1..81.

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 (0,0,0,0,2,0,0,0,0,-1).

Formula

a(n) = 2 a(n-5) - a(n-10).

G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 4*x^5 + 3*x^6 + 2*x^7 + x^8 + 5*x^9)/((1 - x)*(1 + x + x^2 + x^3 + x^4))^2.

a(n)=n unless n=0 (mod 5) in which case a(n)=2n-5.

Mathematica

LinearRecurrence[{0, 0, 0, 0, 2, 0, 0, 0, 0, -1}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 15}, 90] (* Harvey P. Dale, Jul 31 2022 *)

Crossrefs

Cf. A222256-A222260.

Sequence in context: A033081 A032579 A151543 * A242415 A242420 A242419

Adjacent sequences: A222258 A222259 A222260 * A222262 A222263 A222264

Keyword

nonn

Author

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

Status

approved