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.

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?

Links

Table of n, a(n) for n=1..84.

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

Adjacent sequences: A353320 A353321 A353322 * A353324 A353325 A353326

Keyword

nonn

Author

Rémy Sigrist, Apr 12 2022

Status

approved