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A365393
Lexicographically earliest infinite sequence such that a(i) = a(j) => A364492(i) = A364492(j) for all i, j >= 0, where A364492(n) is the denominator of n / A163511(n).
6
1, 2, 2, 1, 2, 3, 1, 4, 2, 5, 3, 6, 1, 7, 4, 8, 2, 9, 5, 10, 3, 6, 6, 11, 1, 3, 7, 12, 4, 13, 8, 14, 2, 9, 9, 10, 5, 15, 10, 16, 3, 17, 6, 18, 6, 11, 11, 19, 1, 20, 3, 21, 7, 22, 12, 8, 4, 13, 13, 23, 8, 24, 14, 25, 2, 26, 9, 27, 9, 28, 10, 29, 5, 30, 15, 16, 10, 31, 16, 32, 3, 6, 17, 33, 6, 31, 18, 34, 6, 35, 11
OFFSET
0,2
COMMENTS
Restricted growth sequence transform of A364492.
Question: Which sets of numbers cause the finite branches that grow off-angle from the rays emanating from the origin in the scatter plot, and why the sudden bends in some of them? Compare also to the scatter plot of A365431.
LINKS
FORMULA
For all n >= 1, a(n) = a(2*n) = a(A000265(n)).
PROG
(PARI)
up_to = 65537;
rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om, invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om, invec[i], i); outvec[i] = u; u++ )); outvec; };
A163511(n) = if(!n, 1, my(p=2, t=1); while(n>1, if(!(n%2), (t*=p), p=nextprime(1+p)); n >>= 1); (t*p));
A364492(n) = { my(u=A163511(n)); (u/gcd(n, u)); };
v365393 = rgs_transform(vector(1+up_to, n, A364492(n-1)));
A365393(n) = v365393[1+n];
CROSSREFS
KEYWORD
nonn,look
AUTHOR
Antti Karttunen, Sep 06 2023
STATUS
approved