A231470 -id:A231470 - cp's OEIS frontend

A231155 Largest k such that no sum of digits is divisible by n (zeros not allowed in the digits of k).

9, 88, 999, 9999, 77777, 999999, 9999999, 88888888, 999999999, 9999999999, 77777777777, 999999999999, 9999999999999, 88888888888888, 999999999999999, 9999999999999999, 77777777777777777, 999999999999999999, 9999999999999999999

Offset: 2

Jon Perry, Nov 04 2013

a(n) has fewer than n digits, a special case of the fact that n integers always contain a sub(multi)set with a sum divisible by n.
The single digits appear to be periodic with period 210. - T. D. Noe, Nov 05 2013
This follows from the formula. Note also that the only digits which appear are 1, 5, 7, 8, and 9. - Charles R Greathouse IV, Nov 06 2013

			a(4) = 999 because none of 9, 9+9 or 9+9+9 are divisible by 4. All integers greater than 999 (with no zeros) have the property that some digit sum is divisible by 4, e.g., 1235 has 3+1.

Subsequence of A010785.

a(n)=forstep(k=9,1,-1,if(gcd(n,k)==1, return(10^(n-1)\9*k))) \\ Charles R Greathouse IV, Nov 05 2013

a(n) consists of n-1 digits of d where d is the largest digit such that GCD(n,d)=1.

a(n) = A231470(n)*(10^(n-1)-1)/9. - M. F. Hasler, Nov 09 2013

a(9)-a(20) from Charles R Greathouse IV, Nov 05 2013

A231471 Largest integer less than 11 and coprime to n.

Original entry on oeis.org

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

Offset: 1

M. F. Hasler, Nov 09 2013

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

			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.

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

Cf. A231475 (analog for 5), A231470 (analog for 10), A231155.

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

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

a(n,m=11)=for(k=1,m,gcd(n,m-k)==1&&return(m-k))

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

A231155 Largest k such that no sum of digits is divisible by n (zeros not allowed in the digits of k).

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A231471 Largest integer less than 11 and coprime to n.

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A231475 Largest integer less than 5 and coprime to n.

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A231472 Largest integer less than 12 and coprime to n.

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