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A203572 Period length 12: 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1 repeated. 2
0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence can be continued periodically for negative values of n.

This is the sixth sequence of a k-family of sequences P_k, k>=1, which starts with A000007(n+1), n>=0, (the 0-sequence), A000035, A193680, A193682, A203571 for k=1,...,5, respectively.

See a comment on A203571 for the general case of the P_k sequences. For a(n)=P_6(n) the nonnegative members of the equivalence classes [0], [1],...,[5], defined by p==q iff P_6(p)=P_6(q), are found in the array A092260 if there class [6], starting with 6, is replaced by 0,6,12,..., which is class [0] (nonnegative part).

LINKS

Table of n, a(n) for n=0..60.

FORMULA

a(n) = n(mod 6) if (-1)^floor(n/6)=+1 else (6-n)(mod 6), n>=0. (-1)^floor(n/6) is the sign corresponding to the parity of the quotient floor(n/6). This quotient is sometimes denoted by n\6.

O.g.f.: x*(1+2*x+3*x^2+4*x^3+5*x^4+5*x^6+4*x^7+3*x^8+2*x^9+ x^10)/(1-x^12).

EXAMPLE

a(14) = 14(mod 6) = 2 because 14\6 = floor(14/6)=2 is even; the sign is +1.

a(8) = (6-8)(mod 6) = 4 because 8\6 = floor(8/6)=1 is odd; the sign is -1.

MATHEMATICA

PadRight[{}, 120, {0, 1, 2, 3, 4, 5, 0, 5, 4, 3, 2, 1}] (* Harvey P. Dale, Nov 28 2015 *)

CROSSREFS

Cf. A203571.

Sequence in context: A309957 A220660 A257846 * A195829 A095874 A279385

Adjacent sequences:  A203569 A203570 A203571 * A203573 A203574 A203575

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jan 12 2012

STATUS

approved

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Last modified June 17 17:41 EDT 2021. Contains 345085 sequences. (Running on oeis4.)