OFFSET
1,1
COMMENTS
See the network with the 50 smallest merging points of A334245 in link.
LINKS
Robert Israel, Table of n, a(n) for n = 1..5939
Bernard Schott and Blandine Schott, Network of merging points.
EXAMPLE
l means: add least prime factor, and,
L means: add largest prime factor.
For 3:
L: 3 + 3 = 6 l: 3 + 3 = 6
l: 6 + 2 = 8 L: 6 + 3 = 9
L: 8 + 2 = 10 l: 9 + 3 = 12
l: 10 + 2 = 12
So A334245(3) = 12 and 12 is a merging point with a(1) = 12.
Now, for 12:
L: 12 + 3 = 15 l: 12 + 2 = 14
l: 15 + 3 = 18 L: 14 + 7 = 21
L: 18 + 3 = 21
So A334245(12) = 21 and 21 is the merging point corresponding to 12 with a(3) = 21.
MAPLE
N:= 1000: # to get all values <= N
S:= x -> x + min(numtheory:-factorset(x)):
T:= x -> x + max(numtheory:-factorset(x)):
f:= proc(n) g(S(n), T(n), 0, 1) end proc:
g:= proc(s, t, i, j) option remember;
if max(s, t) > N then return 0 fi;
if s = t and i=j then return s fi;
if s <= t then
if i = 0 then procname(T(s), t, 1, j)
else procname(S(s), t, 0, j)
fi
elif j=0 then procname(s, T(t), i, 1)
else procname(s, S(t), i, 0)
fi
end proc:
sort(convert(map(f, {$2..N}) minus {0}, list)); # Robert Israel, Jul 09 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, Jun 27 2020
STATUS
approved