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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

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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