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A285298 Number of 10's found in the first differences of a reduced residue system modulo a primorial p#.

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%I A285298 #14 Nov 14 2023 04:35:48
%S A285298 0,0,0,2,30,438,7734,148530,3401790,97648950,2985436650,108861586050,
%T A285298 4396116829650,186022750845750,8604610718954250,449203003036037250,
%U A285298 26126835342151293750,1570919774837171508750,103827535054074567986250,7274630596396103444253750
%N A285298 Number of 10's found in the first differences of a reduced residue system modulo a primorial p#.
%C A285298 Technically, the formula is undefined modulo 2# or 3#, but I have listed their values as "0", since there are no 10's in the first differences of their reduced residue systems. For our purposes, by "10's", we mean n such that n,n+10 are relatively prime to the primorial modulus, while n+1,n+2,n+3,n+4,n+5,n+6,n+7,n+8,n+9 all share a factor (or factors) with p#.
%H A285298 Steven Brown, <a href="https://arxiv.org/abs/2311.06873">Distance between consecutive elements of the multiplicative group of integers modulo n</a>, arXiv:2311.06873 [math.NT], 2023. See Table 1 p. 25.
%F A285298 a(n) = 4*product(p-2) - 6*product(p-3) + 2*product(p-4), where p runs through the primes > 5 and <= prime(n).
%t A285298 Table[4*Product[-2 + Prime[z], {z, 4, i}] -
%t A285298    6*Product[-3 + Prime[z], {z, 4, i}] +
%t A285298    2*Product[-4 + Prime[z], {z, 4, i}], {i, 20}]
%Y A285298 Cf. A059861, A271564, A271565.
%K A285298 nonn
%O A285298 1,4
%A A285298 _Andrew Fuchs_, Apr 16 2017