cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-5 of 5 results.

A076362 Smallest x such that A061498(x)=n: least number in dRRS of which n distinct term occur.

Original entry on oeis.org

1, 3, 9, 15, 385, 105, 3003, 1155, 51051, 36465, 15015, 692835, 440895, 255255, 10140585, 8580495, 4849845
Offset: 0

Views

Author

Labos Elemer, Oct 09 2002

Keywords

Comments

Is it a rule that in each dRRS[a(n)], distinct differences are {1,2,...,n}?
No more terms up to 2*10^5. - Michel Marcus, Mar 26 2020
a(17) > 2.4*10^7. a(18) <= 248834355, a(19) <= 190285095, a(20) <= 111546435. - Giovanni Resta, Apr 13 2020

Examples

			n=5, a(5)=105 because in dRRS[105]={1,2,4,3,2,....,1,5,...,2,1} five distinct terms[=consecutive residue-differences] occur, namely: {1,2,3,4,5}.

Crossrefs

Cf. A061498, A000010.

Programs

  • Mathematica
    gw[x_] := Table[GCD[w, x], {w, 1, x}] rrs[x_] := Flatten[Position[gw[x], 1]] dr[x_] := Delete[RotateLeft[rrs[x]]-rrs[x], -1] did[x_] := Length[Union[dr[x]]] t=Table[0, {25}]; Do[s=did[n]; If[s<258&&t[[s]]==0, t[[s]]=n], {n, 1, 100000}]; t

Formula

a(n) = Min{x; A061498(x)=n}.

Extensions

a(8)-a(10) from Michel Marcus, Mar 25 2020
a(11)-a(16) from Giovanni Resta, Apr 13 2020

A076363 a(n) = A000010(n) - A061498(n).

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 5, 3, 4, 2, 9, 2, 11, 4, 5, 7, 15, 4, 17, 6, 9, 8, 21, 6, 18, 10, 16, 10, 27, 5, 29, 15, 17, 14, 21, 10, 35, 16, 21, 14, 39, 9, 41, 18, 21, 20, 45, 14, 40, 18, 29, 22, 51, 16, 37, 22, 33, 26, 57, 13, 59, 28, 33, 31, 45, 17, 65, 30, 41, 21, 69, 22, 71, 34, 37, 34
Offset: 1

Views

Author

Labos Elemer, Oct 09 2002

Keywords

Crossrefs

Cf. A000010, A061498.

Programs

  • PARI
    a061498(n) = {my(va = select(x->(gcd(n, x)==1), [1..n])); vd = vector(#va-1, k, va[k+1] - va[k]); #Set(vd);}
a(n) = eulerphi(n) - a061498(n); \\ Michel Marcus, Jul 08 2018

A076364 Number of distinct terms in dRRS equals 2: A061498(x)=2.

Original entry on oeis.org

9, 10, 12, 14, 18, 20, 22, 24, 25, 26, 27, 28, 34, 36, 38, 40, 44, 46, 48, 49, 50, 52, 54, 56, 58, 62, 68, 72, 74, 76, 80, 81, 82, 86, 88, 92, 94, 96, 98, 100, 104, 106, 108, 112, 116, 118, 121, 122, 124, 125, 134, 136, 142, 144, 146, 148, 152, 158, 160, 162, 164
Offset: 1

Views

Author

Labos Elemer, Oct 09 2002

Keywords

Comments

2p and prime powers are here.

Crossrefs

Cf. A000010, A061498.

Programs

  • PARI
    isok(n) = {my(va = select(x->(gcd(n, x)==1), [1..n])); vd = vector(#va-1, k, va[k+1] - va[k]); #Set(vd) == 2;} \\ Michel Marcus, Mar 30 2020

A070971 a(n) is the smallest positive integer m for which A070194(m) (i.e., the maximal gap in {k|gcd(k,m) = 1, 1 <= k <= m-1}) is n.

Original entry on oeis.org

3, 4, 15, 6, 105, 30, 1155, 770, 36465, 210, 15015, 6006, 255255, 2310, 8580495, 102102, 4849845, 72930, 20056049013, 74364290, 5898837945, 30030, 3234846615, 881790, 195282582495, 510510, 218257003965, 20281170, 100280245065, 17160990, 934482952262145, 6614136163635
Offset: 1

Views

Author

John W. Layman, May 17 2002

Keywords

Comments

a(n) is the least x such that maximal gap in RRS of x equals n: a(n) = max{x: A070194(x) = n}
For n > 2, same as A128759, which gives the least k such that the Jacobsthal function A048669(k) equals n. See A128759 for more comments. - T. D. Noe, Mar 28 2007

Examples

			A070194 begins with 1,2,1,4,... with offset 3, so a(4)=6.

Crossrefs

Cf. A000010, A061498, A070194, A071194.

Programs

  • Mathematica
    gw[x_] := Table[GCD[w, x], {w, 1, x}] rrs[x_] := Flatten[Position[gw[x], 1]] dr[x_] := Delete[RotateLeft[rrs[x]]-rrs[x], -1] t=Table[0, {25}]; Do[s=Max[dr[n]]; If[s<26&&t[[s]]==0, t[[s]]=n], {n, 3, 10000}]; t (* Labos Elemer, Oct 09 2002 *)

Extensions

a(13)-a(18) from T. D. Noe, Mar 28 2007
a(19) onwards from Don Reble, Oct 17 2013

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

Original entry on oeis.org

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
Offset: 1

Views

Author

Jamie Morken, Nov 21 2019

Keywords

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

Examples

			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.

Links

Crossrefs

Cf. A061498, A048670, A309497, A286941, A331118.

Programs

  • 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 *)
  • 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

Formula

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

Extensions

a(12)-a(44) from Jamie Morken, Jul 11 2020 (after Mario Ziller)
Showing 1-5 of 5 results.

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