cp's OEIS Frontend

A329815 Number of distinct terms in the first difference sequence of the reduced residue system of the n-th primorial.

%I A329815 #54 Aug 05 2020 08:23:24
%S A329815 0,1,3,5,7,10,13,16,20,23,29,33,37,43,49,53,59,66,75,84,92,99,108,116,
%T A329815 127,132,140,148,156,164,174,185,193,206,215,224,235,245,255,267,275,
%U A329815 286,297,308
%N A329815 Number of distinct terms in the first difference sequence of the reduced residue system of the n-th primorial.
%C A329815 This sequence is the number of distinct terms in the first difference sequence for rows n in A286941 and A309497.
%C A329815 Number of distinct terms listed in row n of A331118. - _Michael De Vlieger_, Jul 11 2020
%H A329815 Mario Ziller, <a href="https://arxiv.org/abs/2007.01808">On differences between consecutive numbers coprime to primorials</a>, arXiv:2007.01808 [math.NT], 2020.
%F A329815 a(n) = A061498(A002110(n)).
%F A329815 a(n) <= A048670(n)/2.
%e A329815 For n = 3, A002110(3) = 30, RRS = {1, 7, 11, 13, 17, 19, 23, 29}, dRRS = {6, 4, 2, 4, 2, 4, 6}, so a(3) = 3.
%t A329815 Primorial[n_] := Times @@ Prime[Range[n]]; Table[Length@ Union@ Differences@ Select[Range@ Primorial[n], CoprimeQ[#, Primorial[n]] &], {n, 7}] (* after _Michael De Vlieger_ Jul 15 2017 from A061498 *)
%o A329815 (PARI) f(n) = {my(va = select(x->(gcd(n, x)==1), [1..n])); vd = vector(#va-1, k, va[k+1] - va[k]); #Set(vd); } \\ A061498
%o A329815 a(n) = f(prod(i=1, n, prime(i))); \\ _Michel Marcus_, Dec 19 2019
%Y A329815 Cf. A061498, A048670, A309497, A286941, A331118.
%K A329815 nonn,hard
%O A329815 1,3
%A A329815 _Jamie Morken_, Nov 21 2019
%E A329815 a(12)-a(44) from _Jamie Morken_, Jul 11 2020 (after Mario Ziller)