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Numbers k such that A276086(k) == 1 (mod 6), where A276086 is the primorial base exp-function.
9

%I #27 Dec 12 2022 08:16:38

%S 0,12,24,30,42,54,60,72,84,90,102,114,120,132,144,150,162,174,180,192,

%T 204,216,228,246,258,276,288,306,318,336,348,366,378,396,408,420,432,

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

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

%C 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 Antti Karttunen, <a href="/A328632/b328632.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%F {k | A358840(k) == 1}. - _Antti Karttunen_, Dec 02 2022

%o (PARI)

%o A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }

%o A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };

%o A328578(n) = A257993(A276086(A276086(n)));

%o isA328632(n) = (2==A328578(n));

%o (PARI)

%o isA326832(n) = A358841(n);

%o 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 Row 2 of A328631.

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

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

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

%Y Cf. also A328317.

%K nonn

%O 1,2

%A _Antti Karttunen_, Oct 27 2019

%E Definition replaced with a simpler one and the original definition moved to the comments section by _Antti Karttunen_, Dec 03 2022