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A356302 The least k >= 0 such that n and A276086(n+k) are relatively prime, where A276086 is the primorial base exp-function.

%I A356302 #27 Nov 06 2022 19:42:39
%S A356302 0,0,0,3,0,0,0,0,0,3,20,0,0,0,0,15,0,0,0,0,10,3,0,0,0,5,0,3,0,0,0,0,0,
%T A356302 3,0,175,0,0,0,3,20,0,168,0,0,15,0,0,0,161,10,3,0,0,0,5,154,3,0,0,0,0,
%U A356302 0,147,0,0,0,0,0,3,140,0,0,0,0,15,0,2233,0,0,10,3,0,0,126,5,0,3,0,0,0,119,0,3,0,0,0,0,112
%N A356302 The least k >= 0 such that n and A276086(n+k) are relatively prime, where A276086 is the primorial base exp-function.
%C A356302 For all nonzero terms, adding a(n) to n in primorial base generates at least one carry. See the formula involving A329041.
%H A356302 Antti Karttunen, <a href="/A356302/b356302.txt">Table of n, a(n) for n = 0..65537</a>
%H A356302 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%F A356302 a(n) = A356309(n) - n.
%F A356302 If a(n) > 0, then A000035(a(n)) = A000035(n) and A329041(n, a(n)) > 1.
%o A356302 (PARI)
%o A356302 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A356302 A356302(n) = { my(k=0); while(gcd(A276086(n+k),n)!=1,k++); (k); };
%Y A356302 Cf. A276086, A324198, A356309, A329041.
%Y A356302 Cf. A324583 (positions of zeros), A324584 (of nonzeros), A356318 (positions where a(n) > 0 and a multiple of n), A356319 (where 0 < a(n) < n).
%Y A356302 Cf. A358213, A358214 (conjectured positions of records and their values).
%Y A356302 Cf. also A356303, A356304.
%K A356302 nonn,look
%O A356302 0,4
%A A356302 _Antti Karttunen_, Nov 03 2022