A335392 a(n) is the number of ways to reach n by the process of starting from 1 and repeatedly adding 5 or multiplying by 3.

1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 2, 1, 0, 1, 0, 2, 2, 0, 1, 1, 2, 2, 0, 1, 1, 3, 2, 0, 1, 1, 3, 3, 0, 1, 2, 3, 3, 0, 1, 2, 4, 3, 0, 1, 2, 4, 5, 0, 1, 3, 4, 5, 0, 1, 3, 5, 5, 0, 1, 3, 5, 7, 0, 1, 5, 5, 7, 0, 1, 5, 6, 7, 0, 2, 5, 6, 9, 0, 2, 7

Offset

1,18

Comments

This sequence has connections with A018819, the number of ways to reach a number by the process of starting from 1 and repeatedly adding 1 or multiplying by 2.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, Colored logarithmic scatterplot of (n, a(n)) for n = 1..100000 (where the color is function of n mod 5)

Formula

a(n) = 0 iff n belongs to A335365.

a(n) = #{ k > 0 such that A335393(k) = n }.

Example

For n = 18:
- 18 can be expressed as (1+5)*3 and 1*3 + 5 + 5 + 5,
- so a(18) = 2.

Prog

(PARI) for (n=1, #a=vector(87), print1 (a[n]=if (n==1, 1, if (n-5>0, a[n-5], 0)+if (n%3==0, a[n/3], 0))", "))

Crossrefs

Cf. A018819, A335365, A335393.

Sequence in context: A376362 A166347 A055300 * A156256 A029406 A158461

Adjacent sequences: A335389 A335390 A335391 * A335393 A335394 A335395

Keyword

nonn

Author

Rémy Sigrist, Jun 05 2020

Status

approved