A231471 -id:A231471 - cp's OEIS frontend

A231470 Largest integer less than 10, coprime to n.

9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 5, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 5, 9, 9, 8, 9, 9, 7, 9, 9, 8, 9, 9, 7, 9, 9

Offset: 1

M. F. Hasler, Nov 09 2013

Periodic with period 210.
Motivated by A231155(n)=a(n)*(10^(n-1)-1)/9.
a(n) is in {1, 5, 7, 8, 9}. Average value is 253/30 = 8.433.... - Charles R Greathouse IV, Oct 13 2022

			a(210)=1 because 210=2*3*5*7 is not coprime to any number n>1, n<10.

Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, order 210.

Cf. A231475 (analog for 5), A231471 (analog for 11), A231155.

lgi[n_]:=Module[{k=9},While[!CoprimeQ[n,k],k--];k]; Array[lgi,100] (* Harvey P. Dale, Dec 26 2024 *)

a(n)=for(k=1,9,gcd(n,10-k)==1&&return(10-k))

a(n)=n=n%210; (2456570291879305656378327950088507572292988734220585220471023291179171177166614 45448973642646595615830994341498146323777941833948520102560885856758200689935551 394284409822886865709103348710416026442401 \ 9^n)%9+1 \\ Charles R Greathouse IV, Oct 13 2022

A231475 Largest integer less than 5 and coprime to n.

Original entry on oeis.org

4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4, 3, 4, 1, 4, 3, 4

Offset: 1

M. F. Hasler, Nov 09 2013

			a(1)=4 because this is the largest integer less than 5 and it's coprime to n=1.
a(2)=3 because 4 is not coprime to 2 but 3 is.
a(6)=1 because no other positive integer n<4 is coprime to 6=2*3.

Antti Karttunen, Table of n, a(n) for n = 1..65537
Wikipedia, GCD

Cf. A231471 (analog for 11), A231470 (analog for 10), A231155.

Max[Table[If[CoprimeQ[#,d],d,0],{d,4}]]&/@Range[100] (* Harvey P. Dale, Aug 27 2022 *)

A231475(n, m=5) = for(k=1, m, gcd(n, m-k)==1&&return(m-k));

a(2k+1) = 4 = 2*2.

a(2k) = 1 if 3|k, otherwise a(2k)=3. - Jon Perry, Nov 09 2013

A231472 Largest integer less than 12 and coprime to n.

Original entry on oeis.org

11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 7, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 10

Offset: 1

M. F. Hasler, Nov 09 2013

Values in this sequence are 1, 5, 7, 8, 9, 10, and 11; the average value is 3569/330 = 10.81515.... - Charles R Greathouse IV, Aug 19 2016

			a(1..10)=11 because this is the largest integer less than 12 and it is coprime to n=1,...,10.
a(11)=10 because 11 is not coprime to 11 but 10 is.
a(22)=9 because 11 and 10 are not coprime to 22=2*11.
a(2310)=1 because 2310=2*3*5*7*11 is not coprime to any number n>1, n<12.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Cf. A231471 (analog for 11), A231470 (analog for 10), A231155.

Table[SelectFirst[Range[11,1,-1],CoprimeQ[#,n]&],{n,80}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Mar 02 2018 *)

a(n,m=12)=for(k=1,m,gcd(n,m-k)==1&&return(m-k))

cp's OEIS Frontend

A231470 Largest integer less than 10, coprime to n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

PARI

A231475 Largest integer less than 5 and coprime to n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A231472 Largest integer less than 12 and coprime to n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI