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%I #11 Jun 06 2020 01:51:21
%S 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,
%T 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,
%U 7,0,1,5,5,7,0,1,5,6,7,0,2,5,6,9,0,2,7
%N 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.
%C 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.
%H Rémy Sigrist, <a href="/A335392/b335392.txt">Table of n, a(n) for n = 1..10000</a>
%H Rémy Sigrist, <a href="/A335392/a335392.png">Colored logarithmic scatterplot of (n, a(n)) for n = 1..100000</a> (where the color is function of n mod 5)
%F a(n) = 0 iff n belongs to A335365.
%F a(n) = #{ k > 0 such that A335393(k) = n }.
%e For n = 18:
%e - 18 can be expressed as (1+5)*3 and 1*3 + 5 + 5 + 5,
%e - so a(18) = 2.
%o (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))", "))
%Y Cf. A018819, A335365, A335393.
%K nonn
%O 1,18
%A _Rémy Sigrist_, Jun 05 2020