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

%I A328632 #27 Dec 12 2022 08:16:38
%S A328632 0,12,24,30,42,54,60,72,84,90,102,114,120,132,144,150,162,174,180,192,
%T A328632 204,216,228,246,258,276,288,306,318,336,348,366,378,396,408,420,432,
%U A328632 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
%N A328632 Numbers k such that A276086(k) == 1 (mod 6), where A276086 is the primorial base exp-function.
%C A328632 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.
%C A328632 Numbers k for which A276087(k) is an even number, but not a multiple of three.
%C A328632 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).
%H A328632 Antti Karttunen, <a href="/A328632/b328632.txt">Table of n, a(n) for n = 1..10000</a>
%H A328632 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A328632 {k | A358840(k) == 1}. - _Antti Karttunen_, Dec 02 2022
%o A328632 (PARI)
%o A328632 A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }
%o A328632 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328632 A328578(n) = A257993(A276086(A276086(n)));
%o A328632 isA328632(n) = (2==A328578(n));
%o A328632 (PARI)
%o A328632 isA326832(n) = A358841(n);
%o A328632 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
%Y A328632 Row 2 of A328631.
%Y A328632 After the initial zero, setwise difference A328587 \ A328762. Also setwise difference A008588 \ A358843.
%Y A328632 Positions of 1's in A358840 and A358841 (characteristic function), positions of 2's in A328578.
%Y A328632 Cf. A257993, A276086, A328578, A358845 (= a(n)/6).
%Y A328632 Cf. also A328317.
%K A328632 nonn
%O A328632 1,2
%A A328632 _Antti Karttunen_, Oct 27 2019
%E A328632 Definition replaced with a simpler one and the original definition moved to the comments section by _Antti Karttunen_, Dec 03 2022