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

Author

Antti Karttunen, Sep 07 2023

Keywords

• nonn
• look

Comments

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.

Links

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

Crossrefs

Cf. A005940, A364502, A365432.

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

Programs

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; };
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];