A231475 -id:A231475

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A231470

Largest integer less than 10, coprime to n.

+10
4

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

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

OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..98.

Index entries for linear recurrences with constant coefficients, order 210.

EXAMPLE

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

PROG

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

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

CROSSREFS

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

KEYWORD

nonn,easy

AUTHOR

M. F. Hasler, Nov 09 2013

STATUS

approved

A231471

Largest integer less than 11 and coprime to n.

+10
4

10, 9, 10, 9, 9, 7, 10, 9, 10, 9, 10, 7, 10, 9, 8, 9, 10, 7, 10, 9, 10, 9, 10, 7, 9, 9, 10, 9, 10, 7, 10, 9, 10, 9, 9, 7, 10, 9, 10, 9, 10, 5, 10, 9, 8, 9, 10, 7, 10, 9, 10, 9, 10, 7, 9, 9, 10, 9, 10, 7, 10, 9, 10, 9, 9, 7, 10, 9, 10, 9, 10, 7, 10, 9, 8, 9, 10, 7, 10, 9

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

OFFSET

1,1

COMMENTS

Motivated by the m = 10 analog A231470 which in turn was motivated by A231155, simply a repetition of (n-1) times the same digit A231470(n).

Periodic with period 210. Possible values are 1, 5, 7, 8, 9, 10. - Robert Israel, Jul 03 2020

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 10 because 10 is the largest integer less than 11 and it's coprime to 1.

a(2) = 9 because 10 is not coprime to 2 but 9 is.

a(6) = 7 because 10, 9 and 8 are not coprime to 6 = 2*3.

a(210) = 1 because 210 = 2*3*5*7 is not coprime to any number n > 1, n < 11.

MAPLE

f:= proc(n) local k;

for k from 10 by -1 do if igcd(n, k)=1 then return k fi od

end proc:

map(f, [$1..210]); # Robert Israel, Jul 03 2020

MATHEMATICA

Table[m = 10; While[GCD[m, n] != 1, m--]; m, {n, 75}] (* Alonso del Arte, Nov 09 2013 *)