A328628 Lexicographically earliest infinite sequence such that a(i) = a(j) => A046523(A328624(i)) = A046523(A328624(j)) for all i, j.

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

Offset

0,2

Comments

Restricted growth sequence transform of function f(n) = A046523(A328624(n)) = A278226(A328625(n)).

For all i, j:

a(i) = a(j) => A328630(i) = A328630(j).

The scatter plot looks like a mound (or hive) of insects. - Antti Karttunen, Jan 09 2023

Links

Antti Karttunen, Table of n, a(n) for n = 0..32768

Index entries for sequences related to primorial base

Prog

(PARI)
up_to = 32768;
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; };
A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ From A046523
A328624(n) = { my(m=1, p=2, e, g=1); while(n, e = (n%p); m *= (p^((g*e)%p)); g = e+1; n = n\p; p = nextprime(1+p)); (m); };
Aux328628(n) = A046523(A328624(n));
v328628 = rgs_transform(vector(1+up_to, n, Aux328628(n-1)));
A328628(n) = v328628[1+n];

Crossrefs

Cf. A046523, A278226, A328624, A328625, A328629, A328630.

Sequence in context: A357378 A351257 A286626 * A328629 A342022 A226078

Adjacent sequences: A328625 A328626 A328627 * A328629 A328630 A328631

Keyword

nonn,look

Author

Antti Karttunen, Oct 25 2019

Status

approved