cp's OEIS Frontend

Index of the least significant zero digit in the primorial base expansion of A276086(n), when the rightmost digit is in the position 1.

The scatter plot shows both regular looking as well as more chaotic regions. This can be more clearly seen in related A328579. See also A328839.

Numbers n for which A257993(n) is equal to A328578(n).

All odd numbers are included, as A257993(2n+1) = A328578(2n+1) = 1 for all n >= 0.

Numbers k >= 0 for which A328578(k) = A257993(A276086(A276086(k))) = 2, where A276086 converts the primorial base expansion of k into its prime product form, and A257993 returns the index of the least prime not present in its argument. - The original, equivalent definition.

Numbers k for which A276087(k) is an even number, but not a multiple of three.

All terms are multiples of 6, and thus apart from the initial zero, this is a subsequence of A328587, numbers k for which A257993(A276086(A276086(k))) is less than A257993(k).

All terms are multiples of 6, but very few multiples of 5 (and thus of 10) are present: the first ones are at a(169) = 2520 and a(254) = 3780. Among the first 10000 terms, there are only 28 ending with decimal digit 0, while those that end with either 2 or 4 are 2450 both, and with either 6 or 8, both have 2536 each.

Other multiples of six are in A328587 and A328589.

Numbers n for which A328578(n) > A257993(n).

A047235 (numbers that are congruent to {2, 4} mod 6, thus even numbers that are not multiples of 3, with A257993(n) = 1) is a subsequence, because in primorial base (A049345) such numbers end with digits "10" or "20". A276086 will convert such a number to a number of the form p_k^e_k * ... * 7^b * 5^a * 3^{1,2} * 2^0 (an odd multiple of three, thus of the form 6k+3) which in primorial base will end with digits "11", thus on the second iteration A276086 will convert that to a number of the form p_k^e_k * ... * 7^b * 5^a * 3^1 * 2^1, with the least missing prime having an index (A257993) at least 3, which is larger than the original 1. Thus all terms of A047235 are included in this sequence.

Multiples of six such that the least nondivisor prime of the original n is less than the least nondivisor prime of the number obtained after two iterations of A276086 is.

All terms are multiples of 5 (and thus of 30), because when applied to any number which is a multiple of 6, but not of 5 (and thus not a multiple of 30, so the primorial expansion ends with "x00", where x <> 0, and A257993(n) = 3), A276086 will yield a number of the form 30k+5 or 30k+25 (A084967) whose primorial expansion ends either as "...021" or as "...401" (with the least significant zero either in position 2 or 3), thus then A328578(n) = A257993(A276086(A276086(n))) is definitely not larger than 3, while A257993(6k) >= 3 for all k >= 1.

All terms are multiples of 5 (and thus of 30), because when applied to any number which is a multiple of 6, but not of 5 (and thus not a multiple of 30, implying that the primorial expansion ends with "x00", where x <> 0, and A257993(n) = 3), A276086 will yield a number of the form 30k+5 or 30k+25 (A084967) whose primorial expansion ends either as "...021" or as "...401" (with the least significant zero either in position 2 or 3), thus A328578(n) = A257993(A276086(A276086(n))) cannot simultaneously be larger than 2 and smaller than A257993(n).