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A335906
Number of distinct integers encountered on all possible paths from n to any first encountered powers of 2 (that are included in the count), when using the transitions x -> x - (x/p) and x -> x + (x/p) in any order, where p is the largest prime dividing x.
4
1, 1, 3, 1, 4, 3, 4, 1, 6, 4, 5, 3, 5, 4, 7, 1, 7, 6, 8, 4, 7, 5, 6, 3, 9, 5, 10, 4, 9, 7, 8, 1, 8, 7, 9, 6, 9, 8, 8, 4, 9, 7, 10, 5, 11, 6, 7, 3, 9, 9, 11, 5, 13, 10, 10, 4, 12, 9, 10, 7, 9, 8, 11, 1, 10, 8, 10, 7, 9, 9, 10, 6, 10, 9, 13, 8, 11, 8, 10, 4, 15, 9, 10, 7, 13, 10, 13, 5, 14, 11, 10, 6, 12, 7, 15, 3, 10, 9, 12, 9, 15, 11, 14, 5, 13
OFFSET
1,3
LINKS
EXAMPLE
From 9 one can reach with the transitions x -> A171462(x) (leftward arrow) and x -> A335876(x) (rightward arrow) the following six numbers, when one doesn't expand any power of 2 further:
9
/ \
6 12
/ \ / \
4 8 16
thus a(9) = 6.
From 10 one can reach with the transitions x -> A171462(x) and x -> A335876(x) the following for numbers, when one doesn't expand any power of 2 further:
10
|\
| \
| 12
| /\
|/ \
8 16
thus a(10) = 4.
From 15 one can reach with the transitions x -> A171462(x) and x -> A335876(x) the following seven numbers, when one doesn't expand any power of 2 further:
15
/ \
/ \
12<----18
/ \ \
/ \ \
8 16<----24
\
\
32
thus a(15) = 7.
PROG
(PARI)
A171462(n) = if(1==n, 0, (n-(n/vecmax(factor(n)[, 1]))));
A335876(n) = if(1==n, 2, (n+(n/vecmax(factor(n)[, 1]))));
A209229(n) = (n && !bitand(n, n-1));
A335906(n) = { my(xs=Set([n]), allxs=xs, newxs, a, b, u); for(k=1, oo, newxs=Set([]); if(!#xs, return(#allxs)); allxs = setunion(allxs, xs); for(i=1, #xs, u = xs[i]; if(!A209229(u), newxs = setunion([A171462(u)], newxs); newxs = setunion([A335876(u)], newxs))); xs = newxs); };
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jun 30 2020
STATUS
approved