

A078734


Start with 1,2, concatenate 2^k previous terms and change last term as follows: 1>2, 2>3, 3>1.


1



1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 2, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 1, 1
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OFFSET

1,2


LINKS

Andrew Howroyd, Table of n, a(n) for n = 1..1024


FORMULA

Sum_{k=1..n} a(k))/n > 1.57....
Multiplicative with a(2^e) = (e mod 3) + 1, a(p^e) = 1 for odd prime p.  Andrew Howroyd, Jul 31 2018


EXAMPLE

Concatenating the first 2 terms 1,2 > 1,2,1,2 and changing 2>3 gives the first 4 terms: 1,2,1,3.
Concatenating those first 4 terms >1,2,1,3,1,2,1,3 and changing 3>1 gives the first 8 terms: 1,2,1,3,1,2,1,1.


PROG

(PARI) seq(n)={my(v=[1, 2]); while(#v < n, v=concat(v, v); v[#v] = v[#v] % 3 + 1); vector(n, i, v[i])} \\ Andrew Howroyd, Jul 31 2018
(PARI) a(n) = valuation(n, 2) % 3 + 1; \\ Andrew Howroyd, Jul 31 2018
(MAGMA) [Valuation(n, 2) mod 3 + 1: n in [1..100]]; // Vincenzo Librandi, Aug 01 2018


CROSSREFS

Cf. A056832, A035263.
Sequence in context: A092412 A265578 A279288 * A028293 A092782 A119647
Adjacent sequences: A078731 A078732 A078733 * A078735 A078736 A078737


KEYWORD

nonn,mult


AUTHOR

Benoit Cloitre, Dec 21 2002


STATUS

approved



