cp's OEIS Frontend

Numbers n for which A328578(n) is less than A257993(n).

All terms are multiples of 6. The final digit {0, 2, 4, 6, 8} of the decimal representation seems to be quite evenly distributed.

Other multiples of six are in A328586 and A328589.

210 is the first term not present in A328632.

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.

Numbers n for which A276087(n) is a multiple of 6, but not of 5.

Question: Is the even bisection of A328316, starting from A328316(4) as: 6, 18, 43218, ..., a subsequence of this sequence? See also A328317.

Subsequence such that both k and A276087(k) are in this sequence starts as: 2, 6, 18, 34, 36, 48, 66, 154, 156, 186, 234, 244, 294, 312, 324, 354, 364, 384, 426, 438, 454, 456, 542, 546, 558, 588, 606, ...

When A276086 is applied to any number which is a multiple of 6, but not of 5 (and thus not a multiple of 30, implying that the number's primorial expansion ends with "x00", where x <> 0, and A257993(n) = 3), the original number will be converted to 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 in position A328578(n), which is seen to be always either 3 or 2.

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).