A329815 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A329815

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

0, 1, 3, 5, 7, 10, 13, 16, 20, 23, 29, 33, 37, 43, 49, 53, 59, 66, 75, 84, 92, 99, 108, 116, 127, 132, 140, 148, 156, 164, 174, 185, 193, 206, 215, 224, 235, 245, 255, 267, 275, 286, 297, 308

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

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

Number of distinct terms listed in row n of A331118. - Michael De Vlieger, Jul 11 2020

LINKS

Table of n, a(n) for n=1..44.

Mario Ziller, On differences between consecutive numbers coprime to primorials, arXiv:2007.01808 [math.NT], 2020.

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(#va-1, 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, A331118.

Sequence in context: A036604 A001768 A327672 * A089108 A186355 A029899

Adjacent sequences: A329812 A329813 A329814 * A329816 A329817 A329818

KEYWORD

nonn,hard

AUTHOR

Jamie Morken, Nov 21 2019

EXTENSIONS

a(12)-a(44) from Jamie Morken, Jul 11 2020 (after Mario Ziller)

STATUS

approved