

A329815


Number of distinct terms in the first difference sequence of the reduced residue system of the nth primorial.


0



0, 1, 3, 5, 7, 10, 13, 16, 20, 23, 29
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OFFSET

1,3


COMMENTS

This sequence is the number of distinct terms in the first difference sequence for rows n in A286941 and A309497.


LINKS

Table of n, a(n) for n=1..11.
Jamie Morken, Mathematica Stack Exchange question


FORMULA

a(n) = A061498(A002110(n)).
a(n) <= A048670(n)/2.


EXAMPLE

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.


MATHEMATICA

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 *)


PROG

(PARI) f(n) = {my(va = select(x>(gcd(n, x)==1), [1..n])); vd = vector(#va1, k, va[k+1]  va[k]); #Set(vd); } \\ A061498
a(n) = f(prod(i=1, n, prime(i))); \\ Michel Marcus, Dec 19 2019


CROSSREFS

Cf. A061498, A048670, A309497, A286941.
Sequence in context: A036604 A001768 A327672 * A089108 A186355 A029899
Adjacent sequences: A329812 A329813 A329814 * A329816 A329817 A329818


KEYWORD

nonn,hard,more


AUTHOR

Jamie Morken, Nov 21 2019


STATUS

approved



