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

Author

Rémy Sigrist, Jun 05 2020

Keywords

• nonn

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.

Examples

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

Crossrefs

Cf. A018819, A335365, A335393.

Programs

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))", "))

Formula

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

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