A365715 -id:A365715 - cp's OEIS frontend

A365431 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364502(i) = A364502(j) for all i, j >= 1, where A364502(n) is the denominator of n / A005940(n).

1, 1, 1, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 2, 2, 1, 6, 3, 7, 1, 8, 4, 9, 1, 10, 5, 5, 2, 11, 2, 12, 1, 13, 6, 14, 3, 15, 7, 7, 1, 16, 8, 17, 4, 18, 9, 19, 1, 20, 10, 10, 5, 21, 5, 9, 2, 22, 11, 23, 2, 24, 12, 25, 1, 26, 13, 27, 6, 28, 14, 29, 3, 30, 15, 6, 7, 5, 7, 31, 1, 32, 16, 33, 8, 16, 17, 17, 4, 34, 18, 35, 9, 36, 19, 12, 1

Offset: 1

Antti Karttunen, Sep 07 2023

Restricted growth sequence transform of A364502, or equally, of A365432.
For all i, j: A003602(i) = A003602(j) => a(i) = a(j).
Compare to the scatter plots of A365393 and A365715.

Antti Karttunen, Table of n, a(n) for n = 1..65537

Cf. A005940, A364502, A365432.

Cf. also A365393, A365715 (analogous sequence for Doudna variant D(3)).

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; };
A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t };
A364502(n) = { my(u=A005940(n)); (u / gcd(n, u)); };
v365431 = rgs_transform(vector(up_to,n,A364502(n)));
A365431(n) = v365431[n];

A365718 Lexicographically earliest infinite sequence such that a(i) = a(j) => A365717(i) = A365717(j) for all i, j >= 0, where A365717(n) = A348717(A356867(1+n)).

Original entry on oeis.org

1, 2, 2, 2, 3, 4, 5, 6, 3, 2, 7, 4, 3, 8, 9, 10, 11, 12, 4, 13, 14, 6, 15, 16, 17, 18, 6, 2, 19, 5, 5, 20, 21, 22, 23, 9, 3, 24, 12, 9, 25, 26, 27, 28, 29, 12, 30, 31, 11, 32, 33, 34, 35, 36, 4, 37, 14, 8, 38, 39, 40, 41, 42, 6, 43, 36, 16, 44, 45, 46, 47, 48, 29, 49, 50, 18, 51, 52, 53, 54, 11, 2, 55, 7, 7, 56

Offset: 0

Antti Karttunen, Sep 17 2023

Restricted growth sequence transform of A365717.
For all i, j >= 0: a(i) = a(j) => A365720(i) = A365720(j).
In contrast to austere A103391, which is easily computed from n's binary expansion, the scatter plot here with its slender seaweed-like branchings suggests that this sequence is not just a simple derivation of base-3 expansion of n.

Antti Karttunen, Table of n, a(n) for n = 0..59049

Cf. A348717, A356867, A365720.

Cf. also A103391 (similar transformation applied to A005940) and A365715 (compare the scatter plot).

up_to = 59049; \\ = 3^10.
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; };
A348717(n) = if(1==n, 1, my(f = factor(n), k = primepi(f[1, 1])-1); for (i=1, #f~, f[i, 1] = prime(primepi(f[i, 1])-k)); factorback(f));
A356867list(up_to) = { my(v=vector(up_to),met=Map(),h=0,ak); for(i=1,#v,if(1==vecsum(digits(i,3)), v[i] = i; h = i, ak = v[i-h]; forprime(p=2,,if(3!=p && !mapisdefined(met,p*ak), v[i] = p*ak; break))); mapput(met,v[i],i)); (v); };
v365718 = rgs_transform(apply(A348717,A356867list(1+up_to)));
A365718(n) = v365718[1+n];

cp's OEIS Frontend

A365431 Lexicographically earliest infinite sequence such that a(i) = a(j) => A364502(i) = A364502(j) for all i, j >= 1, where A364502(n) is the denominator of n / A005940(n).

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