A328632 Numbers k such that A276086(k) == 1 (mod 6), where A276086 is the primorial base exp-function.

0, 12, 24, 30, 42, 54, 60, 72, 84, 90, 102, 114, 120, 132, 144, 150, 162, 174, 180, 192, 204, 216, 228, 246, 258, 276, 288, 306, 318, 336, 348, 366, 378, 396, 408, 420, 432, 444, 450, 462, 474, 480, 492, 504, 510, 522, 534, 540, 552, 564, 570, 582, 594, 600, 612, 624, 636, 648, 666, 678, 696, 708, 726, 738, 756, 768, 786, 798, 816

Offset: 1

Author

Antti Karttunen, Oct 27 2019

Keywords

• nonn

Comments

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).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial base

Crossrefs

Row 2 of A328631.

After the initial zero, setwise difference A328587 \ A328762. Also setwise difference A008588 \ A358843.

Positions of 1's in A358840 and A358841 (characteristic function), positions of 2's in A328578.

Cf. A257993, A276086, A328578, A358845 (= a(n)/6).

Cf. also A328317.

Programs

PARI

A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A328578(n) = A257993(A276086(A276086(n)));
isA328632(n) = (2==A328578(n));

PARI

isA326832(n) = A358841(n);
A358841(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (1==(m%6)); }; \\ Antti Karttunen, Dec 12 2022

Formula

{k | A358840(k) == 1}. - Antti Karttunen, Dec 02 2022

Extensions

Definition replaced with a simpler one and the original definition moved to the comments section by Antti Karttunen, Dec 03 2022