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A006288 Loxton-van der Poorten sequence: base 4 representation contains only -1, 0, +1.
(Formerly M2312)
1
0, 1, 3, 4, 5, 11, 12, 13, 15, 16, 17, 19, 20, 21, 43, 44, 45, 47, 48, 49, 51, 52, 53, 59, 60, 61, 63, 64, 65, 67, 68, 69, 75, 76, 77, 79, 80, 81, 83, 84, 85, 171, 172, 173, 175, 176, 177, 179, 180, 181, 187, 188, 189, 191, 192, 193, 195, 196, 197, 203, 204, 205, 207, 208, 209 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..64.

J.-P. Allouche and J. Shallit, The ring of k-regular sequences, Theoretical Computer Sci., 98 (1992), 163-197. [DOI]

J. H. Loxton and A. J. van der Poorten, Arithmetic properties of automata: regular sequences, J. Reine Angew. Math. 392 (1988), 57-69.

FORMULA

Recurrence: a(3n) = 4a(n), a(3n-1) = 4a(n)-1, a(3n+1) = 4a(n)+1, starting 0,1. - Ralf Stephan, Jan 19 2014

EXAMPLE

1*4^2 + 0*4^1 + (-1)*4^0 = 15, so 15 is in sequence.

PROG

(PARI) a(n)=if(n<2, n>0, 4*a((n+1)\3)+(n+1)%3-1) \\ Ralf Stephan, Jan 19 2014

CROSSREFS

Cf. A023713, A023717.

Sequence in context: A319067 A224503 A128920 * A047598 A283773 A214256

Adjacent sequences:  A006285 A006286 A006287 * A006289 A006290 A006291

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Offset changed to 0 and example added by Ralf Stephan, Jan 19 2014

STATUS

approved

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Last modified January 17 00:44 EST 2019. Contains 319206 sequences. (Running on oeis4.)