A342022 Lexicographically earliest infinite sequence such that a(i) = a(j) => A342002(i) = A342002(j) for all i, j >= 0.

1, 2, 2, 3, 4, 5, 2, 5, 6, 7, 8, 9, 4, 10, 11, 12, 13, 14, 15, 11, 16, 17, 18, 19, 20, 8, 21, 22, 23, 24, 2, 10, 25, 9, 21, 26, 27, 24, 28, 29, 30, 31, 18, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 4, 11, 8, 14, 49, 50, 21, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 7, 62, 63, 64, 65, 66

Offset: 0

Author

Antti Karttunen, Mar 12 2021

Keywords

• nonn
• look

Comments

Restricted growth sequence transform of A342002.

For all i, j >= 1:

a(i) = a(j) => A342017(i) = A342017(j) => A342019(i) = A342019(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 0..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003415, A276086, A327860, A328572, A342002, A342017, A342019.

Cf. also A286626, A328388.

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; };
A342002(n) = { my(s=0, m=1, p=2, e); while(n, e = (n%p); m *= p^(e>0); s += (e/p); n = n\p; p = nextprime(1+p)); (s*m); };
v342022 = rgs_transform(vector(1+up_to,n,A342002(n-1)));
A342022(n) = v342022[1+n];