A122841 -id:A122841 - cp's OEIS frontend

A010875 a(n) = n mod 6.

0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0, 1, 2, 3, 4, 5, 0

Offset: 0

N. J. A. Sloane

Period 6: repeat [0, 1, 2, 3, 4, 5].
The rightmost digit in the base-6 representation of n. - Hieronymus Fischer, Jun 11 2007
[a(n) * a(m)] mod 6 == a(n*m mod 6) == a(n*m). - Jon Perry, Nov 11 2014
If n > 3 and (a(n) is in {0,2,3,4}), then n is not prime. - Jean-Marc Rebert, Jul 22 2015, corrected by M. F. Hasler, Jul 24 2015

Antti Karttunen, Table of n, a(n) for n = 0..65538
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Partial sums: A130484. Other related sequences A130481, A130482, A130483, A130485.

Cf. also A079979, A097325, A122841.

[n mod 6: n in [0..100]]; // Wesley Ivan Hurt, Jul 06 2014

A010875:=n->n mod 6; seq(A010875(n), n=0..100); # Wesley Ivan Hurt, Jul 06 2014

Mod[Range[0, 100], 6] (* Wesley Ivan Hurt, Jul 06 2014 *)

a(n)=n%6 \\ Charles R Greathouse IV, Dec 05 2011

[power_mod(n,3,6 )for n in range(0, 81)] # Zerinvary Lajos, Oct 29 2009

(define (A010875 n) (modulo n 6)) ;; Antti Karttunen, Dec 22 2017

Complex representation: a(n) = (1/6) * (1 - r^n) * Sum_{k = 1..6} k * Product_{1 <= m < 6, m <> k} (1-r^(n-m)), where r = exp((Pi/3)*i) = (1 + sqrt(3)*i)/2 and i = sqrt(-1).
Trigonometric representation: a(n) = (16/3)^2 * (sin(n*Pi/6))^2 * Sum_{k = 1..6} k * Product_{1 <= m < 6, m<>k} (sin((n-m)*Pi/6))^2.
G.f.: g(x) = (Sum_{k = 1..6} k*x^k)/(1-x^6).
Also: g(x) = x*(5*x^6 - 6*x^5 + 1)/((1 - x^6)*(1 - x)^2). - Hieronymus Fischer, May 31 2007
a(n) = (n mod 2) + 2(floor(n/2) mod 3) = A000035(n) +2*A010872(A004526(n));
a(n) = (n mod 3) + 3(floor(n/3) mod 2) = A010872(n) +3*A000035(A002264(n)). - Hieronymus Fischer, Jun 11 2007
a(n) = 2.5 - 0.5*(-1)^n - cos(Pi*n/3) - 3^0.5*sin(Pi*n/3) -cos(2*Pi*n/3) - 3^0.5/3*sin(2*Pi*n/3). - Richard Choulet, Dec 11 2008
a(n) = n^3 mod 6. - Zerinvary Lajos, Oct 29 2009
a(n) = floor(12345/999999*10^(n+1)) mod 10. - Hieronymus Fischer, Jan 03 2013
a(n) = floor(373/9331*6^(n+1)) mod 6. - Hieronymus Fischer, Jan 04 2013
a(n) = 5/2 - (-1)^n/2 - 2*0^((-1)^(n/6 - 1/12 + (-1)^n/12) - (-1)^(n/2 - 1/4 +(-1)^n/4)) + 2*0^((-1)^(n/6 + 1/4 + (-1)^n/12) + (-1)^(n/2 - 1/4 + (-1)^n/4)). - Wesley Ivan Hurt, Jun 23 2015
E.g.f.: -sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) - 2*cosh(x/2)*cos(sqrt(3)*x/2). - Robert Israel, Jul 22 2015

Formulas 1 to 6 re-edited for better readability by Hieronymus Fischer, Dec 05 2011

More terms from Antti Karttunen, Dec 22 2017

A102669 Number of digits >= 2 in decimal representation of n.

Original entry on oeis.org

0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 0, 0, 1, 1, 1

Offset: 0

N. J. A. Sloane, Feb 03 2005

a(n) = 0 iff n is in A007088 (numbers in base 2). - Bernard Schott, Feb 19 2023

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A027868, A054899, A055640, A055641, A102670 - A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564. Partial sums see A102670.

Cf. A000120, A000788, A007088, A023416, A059015 (for base 2).

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=2 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..116); # Emeric Deutsch, Feb 23 2005

Table[Total@ Take[DigitCount@ n, {2, 9}], {n, 0, 104}] (* Michael De Vlieger, Aug 17 2017 *)

Contribution from Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor(n/10^j + 4/5) - floor(n/10^j)), where m = floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(2*10^j) - x^(10*10^j))/(1 - x^10^(j+1)).
General formulas for the number of digits >= d in the decimal representations of n, where 1 <= d <= 9:
a(n) = Sum_{j=1..m+1} (floor(n/10^j + (10-d)/10) - floor(n/10^j)), where m = floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(d*10^j) - x^(10*10^j))/(1 - x^10^(j+1)). (End)

More terms from Emeric Deutsch, Feb 23 2005

A102685 Partial sums of A055640.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 66, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123

Offset: 0

N. J. A. Sloane, Feb 03 2005

nonn

The total number of nonzero digits occurring in all the numbers 0, 1, 2, ... n (in decimal representation). - Hieronymus Fischer, Jun 10 2012

Hieronymus Fischer, Table of n, a(n) for n = 0..10000

Cf. A027868, A054899, A055640, A055641, A102669-A102684, A117804, A122840, A122841, A160093, A160094, A196563, A196564.

Cf. A000120, A000788, A023416, A059015 (for base 2).

From Hieronymus Fischer, Jun 06 2012: (Start)
a(n) = (1/2)*Sum_{j=1..m+1} (floor((n/10^j)+0.9)*(2n + 2 + (0.8 - floor((n/10^j)+0.9))*10^j) - floor(n/10^j)*(2n + 2 - (floor(n/10^j)+1) * 10^j)), where m = floor(log_10(n)).
a(n) = (n+1)*A055640(n) + (1/2)*Sum_{j=1..m+1} ((8*floor((n/10^j)+0.9)/10 + floor(n/10^j))*10^j - (floor((n/10^j)+0.9)^2 - floor(n/10^j)^2)*10^j), where m = floor(log_10(n)).
a(10^m-1) = 9*m*10^(m-1). (This is the total number of nonzero digits occurring in all the numbers with <= m digits.)
G.f.: g(x) = (1/(1-x)^2) * Sum_{j>=0} (x^10^j - x^(10*10^j))/(1-x^10^(j+1)). (End)

A160094 a(n) = 1 + A122840(n).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1

Offset: 1

Anonymous, May 01 2009

a(n) is the Levenshtein distance from the decimal expansion of n - 1 to the decimal expansion of n. For example, to convert "9" to "10", substitute "0" for "9" and insert "1". Since two such operations are required, a(10) = 2. See the analogous A091090 (binary expansion) and A115777 (full definition). - Rick L. Shepherd, Mar 25 2015

			a(160) = 2 because the last nonzero digit of 160 (counting from left to right), when 160 is written in base 10, is 6, and that 6 occurs 2 digits from the right in 160.

Rick L. Shepherd, Table of n, a(n) for n = 1..10000

Cf. A054899, A055640, A055641, A102669, A122840, A122841, A160093, A196563, A196564, A091090, A115777.

IntegerExponent[Range[150]]+1 (* Harvey P. Dale, Feb 06 2015 *)

From Hieronymus Fischer, Jun 08 2012: (Start)
With m = floor(log_10(n)), frac(x) = x-floor(x):
a(n) = Sum_{j=0..m} (1 - ceiling(frac(n/10^j))).
a(n) = m + 1 + Sum_{j=1..m} (floor(-frac(n/10^j))).
a(n) = 1 + A054899(n) - A054899(n-1).
G.f.: g(x) = (x/(1-x)) + Sum_{j>0} x^10^j/(1-x^10^j). (End)
Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 10/9. - Amiram Eldar, Jul 10 2023
a(n) = A122840(10*n). - R. J. Mathar, Jun 28 2025

Name simplified by Jon E. Schoenfield, Feb 26 2014

A160093 Number of digits in n, excluding any trailing zeros.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 3, 3, 3, 3, 3

Offset: 1

Anonymous, May 01 2009

			a(1060000) = 3 because discarding the trailing zeros from 1060000 leaves 106, which is a 3-digit number.

Indranil Ghosh, Table of n, a(n) for n = 1..10000

Cf. A004151, A054899, A055640, A055641, A055642, A102669, A122840, A122841, A160094, A196563, A196564.

lnzd[n_]:=Module[{spl=Last[Split[IntegerDigits[n]]]},If[!MemberQ[ spl,0], IntegerLength[n], IntegerLength[n]-Length[spl]]]; Array[lnzd,110] (* Harvey P. Dale, Jun 05 2013 *)
Table[IntegerLength[n] - IntegerExponent[n, 10], {n, 100}] (* Amiram Eldar, Sep 14 2020 *)

a(n)=if(n==0,1,#digits(n/10^valuation(n,10))) \\ Joerg Arndt, Jan 11 2017

a(n)=logint(n,10)+1-valuation(n,10) \\ Charles R Greathouse IV, Jan 12 2017

def A160093(n):
     return len(str(int(str(n)[::-1]))) # Indranil Ghosh, Jan 11 2017

From Hieronymus Fischer, Jun 08 2012: (Start)
With m = floor(log_10(n)), frac(x) = x-floor(x):
a(n) = 1 + Sum_{j=0..m} ceiling(frac(n/10^j)).
a(n) = 1 - Sum_{j=1..m} (floor(-frac(n/10^j))).
a(n)= A055642(n) + A054899(n-1) - A054899(n).
G.f.: (x/(1-x)) + (1/(1-x))*Sum_{j>0} x^(10^j+1)*(1 - x^(10^j-1))/(1-x^10^j). (End)
a(n) = A055642(A004086(n)). - Indranil Ghosh, Jan 11 2017
a(n) = A055642(A004151(n)). - Amiram Eldar, Sep 14 2020

Simpler definition and changed example from Jon E. Schoenfield, Feb 15 2014

A079979 Characteristic function of multiples of six.

Original entry on oeis.org

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

Offset: 0

Vladimir Baltic, Feb 17 2003

Period 6: repeat [1, 0, 0, 0, 0, 0].
a(n)=1 if n=6k, a(n)=0 otherwise.
Decimal expansion of 1/999999.
Number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=3, r=3, I={-2,-1,0,1,2}.
Also, number of permutations satisfying -k <= p(i)-i <= r and p(i)-i not in I, i=1..n, with k=1, r=5, I={0,1,2,3,4}.
a(n) is also the number of partitions of n such that each part is six (a(0)=1 because the empty partition has no parts to test equality with six). Hence a(n) is also the number of 2-regular graphs on n vertices with each part having girth exactly six. - Jason Kimberley, Oct 10 2011
This sequence is the Euler transformation of A185016. - Jason Kimberley, Oct 10 2011

D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial theory and its applications, II (Proc. Colloq., Balatonfured, 1969), pp. 755-770. North-Holland, Amsterdam, 1970.

Antti Karttunen, Table of n, a(n) for n = 0..65538
Vladimir Baltic, On the number of certain types of strongly restricted permutations, Applicable Analysis and Discrete Mathematics Vol. 4, No 1 (April, 2010), 119-135
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).
Index entries for characteristic functions

Cf. A002524-A002529, A010875, A072827, A072850-A072856, A079955-A080014, A097325, A122841.

Characteristic function of multiples of g: A000007 (g=0), A000012 (g=1), A059841 (g=2), A079978 (g=3), A121262 (g=4), A079998 (g=5), this sequence (g=6), A082784 (g=7).

Magma
```
&cat[[1,0^^5]^^30];
```

A079979 := func; [A079979:n in [0..59]];  // Jason Kimberley, Oct 10 2011

PadRight[{},120,{1,0,0,0,0,0}] (* Harvey P. Dale, Feb 19 2013 *)

a(n)=!(n%6) \\ Charles R Greathouse IV, Oct 10 2011

(define (A079979 n) (if (zero? (modulo n 6)) 1 0)) ;; Antti Karttunen, Dec 22 2017

a(n) = a(n-6).
G.f.: 1/(1-x^6).
a(n) = floor((1/2)*cos(n*Pi/3) + 1/2). - Gary Detlefs, May 16 2011
a(n) = floor(n/6) - floor((n-1)/6). - Tani Akinari, Oct 23 2012
a(n) = (((((v^n - w^n)^2)*(2 - (-1)^n)*(w^(2*n) + w^n - 3))^2 - 144)^2)/20736, where w = (-1+i*sqrt(3))/2, v = (1+i*sqrt(3))/2. - Bogart B. Strauss, Sep 20 2013
E.g.f.: (2*cos(sqrt(3)*x/2)*cosh(x/2) + cosh(x))/3. - Vaclav Kotesovec, Feb 15 2015

More terms from Antti Karttunen, Dec 22 2017

A235127 Greatest k such that 4^k divides n.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1

Offset: 1

Tom Edgar, Jan 03 2014

			Since 4^2 divides 32 and 4^3 does not, we have a(32) = 2. Likewise, since no positive power of 4 divides 9, a(9) = 0.

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

Cf. A004526, A007814, A007949, A122841, A115362, A234957, A244413.

IntegerExponent[Range@ 105, 4] (* Michael De Vlieger, Nov 18 2017 *)

A235127(n) = valuation(n,4); \\ Antti Karttunen, Nov 18 2017

def A235127(n): return (~n&n-1).bit_length()>>1 # Chai Wah Wu, Jul 08 2022

n=100 #change n for more terms
[valuation(i,4) for i in [1..n]]

a(n) = valuation(n,4).
G.f.: Sum_{k>=1} x^(4^k)/(1 - x^(4^k)). - Ilya Gutkovskiy, Jan 28 2017
a(n) = A004526(A007814(n)). - Antti Karttunen, Nov 18 2017
Asymptotic mean: lim_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 1/3. - Amiram Eldar, Jan 17 2022

More terms from Antti Karttunen, Nov 18 2017

A102683 Number of digits 9 in decimal representation of n.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 0, 0, 0, 0

Offset: 0

N. J. A. Sloane, Feb 03 2005

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A007095, A011539, A027868, A054899, A055640, A055641, A102669-A102685, A117804, A122840, A122841, A160093, A160094, A196563, A196564, A235049.
Cf. A102684 (partial sums).
Cf. A000120, A000788, A023416, A059015 (for base 2).

a102683 =  length . filter (== '9') . show
-- Reinhard Zumkeller, Dec 29 2011

p:=proc(n) local b,ct,j: b:=convert(n,base,10): ct:=0: for j from 1 to nops(b) do if b[j]>=9 then ct:=ct+1 else ct:=ct fi od: ct: end: seq(p(n),n=0..116); # Emeric Deutsch, Feb 23 2005

a[n_] := DigitCount[n, 10, 9]; Array[a, 100, 0] (* Amiram Eldar, Jul 24 2023 *)

a(A007095(n)) = 0; a(A011539(n)) > 0. - Reinhard Zumkeller, Dec 29 2011
From Hieronymus Fischer, Jun 10 2012: (Start)
a(n) = Sum_{j=1..m+1} (floor(n/10^j + 1/10) - floor(n/10^j)), where m=floor(log_10(n)).
G.f.: g(x) = (1/(1-x))*Sum_{j>=0} (x^(9*10^j) - x^(10*10^j))/(1-x^10^(j+1)). (End)
a(A235049(n)) = 0. - Reinhard Zumkeller, Apr 16 2014

More terms from Emeric Deutsch, Feb 23 2005

A047253 Numbers that are congruent to {1, 2, 3, 4, 5} mod 6.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 79, 80, 81, 82, 83, 85, 86

Offset: 1

N. J. A. Sloane

Numbers that are not divisible by 6. - Benoit Cloitre, Jul 11 2009

More generally the sequence a(n,m) of numbers not divisible by some fixed integer m >= 2 is given by a(n,m) = n - 1 + floor((n+m-2)/(m-1)). - Benoit Cloitre, Jul 11 2009

Ivan Panchenko, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1).

Cf. A097325, A122841.

a047253 n = n + n `div` 5
a047253_list = [1..5] ++ map (+ 6) a047253_list
-- Reinhard Zumkeller, Nov 10 2013

Select[Table[n,{n,200}],Mod[#,6]!=0&] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2011*)

PARI
```
a(n)= 1+n+n\5
```

a(n)=n-1+floor((n+4)/5) \\ Benoit Cloitre, Jul 11 2009

a(n) = 5 + a(n-5).
G.f.: x*(1+x)*(1+x+x^2)*(x^2-x+1) / ( (x^4+x^3+x^2+x+1)*(x-1)^2 ).
a(n) = n - 1 + floor((n+4)/5). - Benoit Cloitre, Jul 11 2009
A122841(a(n)) = 0. - Reinhard Zumkeller, Nov 10 2013
Sum_{n>=1} (-1)^(n+1)/a(n) = (15-4*sqrt(3))*Pi/36. - Amiram Eldar, Dec 31 2021

Extended by R. J. Mathar, Oct 18 2008

A044102 Multiples of 36.

Original entry on oeis.org

0, 36, 72, 108, 144, 180, 216, 252, 288, 324, 360, 396, 432, 468, 504, 540, 576, 612, 648, 684, 720, 756, 792, 828, 864, 900, 936, 972, 1008, 1044, 1080, 1116, 1152, 1188, 1224, 1260, 1296, 1332, 1368, 1404, 1440, 1476, 1512, 1548, 1584, 1620, 1656, 1692, 1728

Offset: 0

Clark Kimberling

Also, k such that Fibonacci(k) mod 27 = 0. - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 18 2004
A033183(a(n)) = n+1. - Reinhard Zumkeller, Nov 07 2009
A122841(a(n)) > 1 for n > 0. - Reinhard Zumkeller, Nov 10 2013
Sum of the numbers from 4*(n-1) to 4*(n+1). - Bruno Berselli, Oct 25 2018

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,-1).

Cf. A005843, A008600, A033183, A122841, A135631, A167632, A174312.

Subsequence of A008588.

a:=[0,36];; for n in [3..50] do a[n]:=2*a[n-1]-a[n-2]; od; a; # Muniru A Asiru, Oct 25 2018

a044102 = (* 36)
a044102_list = [0, 36 ..]  -- Reinhard Zumkeller, Nov 10 2013

[36*n: n in [0..50]]; // Vincenzo Librandi, May 20 2014

seq(coeff(series(36*x/(1-x)^2,x,n+1), x, n), n = 0 .. 50); # Muniru A Asiru, Oct 25 2018

Range[0, 2000, 36] (* Vladimir Joseph Stephan Orlovsky, May 31 2011 *)
CoefficientList[Series[36 x/(1 - x)^2, {x, 0, 100}], x] (* Vincenzo Librandi, May 20 2014 *)

a(n)=36*n \\ Charles R Greathouse IV, Oct 07 2015

G.f.: 36*x/(1 - x)^2.
a(n) = A167632(n+1). - Reinhard Zumkeller, Nov 07 2009
a(n) = 36*n. - Vincenzo Librandi, Jan 26 2011
From Elmo R. Oliveira, Apr 10 2025: (Start)
E.g.f.: 36*x*exp(x).
a(n) = 18*A005843(n) = 2*A008600(n).
a(n) = 2*a(n-1) - a(n-2). (End)

cp's OEIS Frontend

A010875 a(n) = n mod 6.

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A102669 Number of digits >= 2 in decimal representation of n.

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A102685 Partial sums of A055640.

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A160094 a(n) = 1 + A122840(n).

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A160093 Number of digits in n, excluding any trailing zeros.

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A079979 Characteristic function of multiples of six.

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A235127 Greatest k such that 4^k divides n.