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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.
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, 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
KEYWORD
nonn
AUTHOR
Rémy Sigrist, Jun 05 2020
STATUS
approved