A168186 -id:A168186 - cp's OEIS frontend

A168185 Characteristic function of numbers that are not multiples of 12.

0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 0

Reinhard Zumkeller, Nov 30 2009

a(n+12) = a(n);
a(n) = A000007(A010881(n));
a(A168186(n)) = 1; a(A008594(n)) = 0;
A033444(n) = Sum_{k=0..n} a(k)*(n-k).

Antti Karttunen, Table of n, a(n) for n = 0..65537
Index entries for characteristic functions
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A010881, A145568, A168184, A168182, A168181, A109720, A097325, A011558, A166486, A011655, A000035.

a:=n->`if`(modp(n,12)=0,0,1); seq(a(n),n=0..150); # Muniru A Asiru, Sep 21 2018

If[Divisible[#,12],0,1]&/@Range[0,120] (* Harvey P. Dale, Apr 03 2015 *)

a(n)=!!(n%12) \\ Charles R Greathouse IV, Aug 21 2011

For the general case: the characteristic function of numbers that are not multiples of m is a(n) = floor((n-1)/m) - floor(n/m) + 1, m,n > 0. - Boris Putievskiy, May 08 2013

A023805 Xenodromes: all digits in base 11 are different.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74

Offset: 1

Olivier Gérard

Considering some base b, there are b numbers with 1 digit, (b-1)*(b-1) numbers with 2 digits -- since leading 0's are not allowed and the second digit must avoid the first. There are (b-1)*(b-1)*(b-2) numbers with 3 digits, (b-1)*(b-1)*(b-2)*..*(b-d+1) numbers with d digits, in total b+(b-1)*sum_{d=2..b} (b-1)!/(b-d)! = b+(b-1)^2* 2F0(1,2-b;;-1) = A001339(b-1). The formula is applicable to sequences A023798 - A023810. This sequence here as A001339(11-1) = 98641011 terms. [From R. J. Mathar, Jan 27 2010]

Last term is a(98641011) = 282458553905. - Charles R Greathouse IV, Jun 16 2012

			121 (in decimal) = 100 (base 11) is a member of A168186 but not a member of this sequence. - Robert Munafo, Jan 26 2010
156 is in A023805 but not in A168186. - Franklin T. Adams-Watters, Jan 26 2010

Paolo Xausa, Table of n, a(n) for n = 1..10000

All three of A023805, A160453, A168186 are different.

Select[Range[0, 100], Max[DigitCount[#, 11]] == 1 &] (* Paolo Xausa, Mar 22 2025 *)

A160453 Numbers k which have a prime divisor p such that 1 is the only positive integer which divides k/p^m and is congruent to 1 modulo p, where p^(m+1) does not divide k.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78

Offset: 1

Masahiko Shin, May 14 2009

nonn

The solvability of a group whose order is a(n) can be reduced to the solvability of smaller group using the Sylow theorems, provided the order is not a prime.

80 is not a member of this sequence, but is a member of A168186. - Franklin T. Adams-Watters, Jan 26 2010

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

All three of A023805, A160453, A168186 are different.

is(k)=if(k<12,return(k>0));my(f=factor(k)); for(i=1,#f~, fordiv(k/f[i,1]^f[i,2],d, if(d>1&&d%f[i,1]==1,next(2))); return(1)); 0 \\ Charles R Greathouse IV, Oct 27 2013

Corrected by Charles R Greathouse IV, Oct 27 2013

cp's OEIS Frontend

A168185 Characteristic function of numbers that are not multiples of 12.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Formula

A023805 Xenodromes: all digits in base 11 are different.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

A160453 Numbers k which have a prime divisor p such that 1 is the only positive integer which divides k/p^m and is congruent to 1 modulo p, where p^(m+1) does not divide k.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

Extensions