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A353323
A variant of Van Eck's sequence where we only consider powers of 3: for n >= 0, if a(n) = a(n-3^e) for some e, take the least such e and set a(n+1) = 3^e; otherwise a(n+1) = 0. Start with a(1) = 0.
1
0, 0, 1, 0, 3, 0, 0, 1, 0, 3, 0, 9, 0, 9, 0, 9, 0, 0, 1, 0, 3, 0, 9, 9, 1, 0, 9, 3, 0, 3, 9, 0, 3, 3, 1, 27, 0, 0, 1, 0, 3, 0, 27, 0, 27, 9, 0, 3, 27, 0, 3, 3, 1, 0, 0, 1, 3, 9, 27, 0, 0, 1, 9, 0, 3, 0, 0, 1, 0, 3, 0, 27, 27, 1, 0, 9, 0, 27, 0, 0, 1, 0, 3, 0
OFFSET
1,5
COMMENTS
Will every power of 3 appear in the sequence?
EXAMPLE
a(1) = 0 by definition.
a(2) = 0 as there is only one occurrence of a(1) = 0 so far.
a(3) = 3^0 = 1 as a(2) = a(2-3^0).
a(4) = 0 as there is only one occurrence of a(3) = 1 so far.
a(5) = 3^1 = 3 as a(4) = a(4-3^1).
a(6) = 0 as there is only one occurrence of a(5) = 3 so far.
a(7) = 0 as a(6) <> a(6-3^e) for any admissible e.
a(8) = 3^0 = 1 as a(7) = a(7-3^0).
a(9) = 0 as a(8) <> a(8-3^e) for any admissible e.
PROG
(PARI) { for (n=1, #a=vector(84), for (e=0, oo, m = n-1-d=3^e; if (m<1, break, a[n-1]==a[m], a[n]=d; break)); print1 (a[n]", ")) }
CROSSREFS
Cf. A181391, A353322 (variant for powers of 2).
Sequence in context: A342154 A074936 A035655 * A239446 A036857 A359270
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Apr 12 2022
STATUS
approved