A005009 -id:A005009 - cp's OEIS frontend

A091629 Product of digits associated with A091628(n). Essentially the same as A007283.

6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472

Offset: 1

Enoch Haga, Jan 24 2004

Sequence arising in Farideh Firoozbakht's solution to Prime Puzzle 251 - 23 is the only pointer prime (A089823) not containing digit "1".

The monotonic increasing value of successive product of digits strongly suggests that in successive n the digit 1 must be present.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Tanya Khovanova, Recursive Sequences
Carlos Rivera, Puzzle 251, Pointer primes, The Prime Puzzles and Problems Connection.
Index entries for linear recurrences with constant coefficients, signature (2).

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A007283 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).
Cf. A089823, A091628, A091630, A091631, A091632.
Similar to A003945, A042950, A058764, A087009, A081808.

[3*2^n : n in [1..40]]; // Wesley Ivan Hurt, Jul 17 2020

3*2^Range[1, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)

[3*2^n for n in range(1,51)] # G. C. Greubel, Jan 05 2023

a(n) = 3 * 2^n = product of digits of A091628(n).
From Philippe Deléham, Nov 23 2008: (Start)
a(n) = 6*2^(n-1).
a(n) = 2*a(n-1), with a(1) = 6.
G.f.: 6*x/(1-2*x). (End)
E.g.f.: 3*(exp(2*x) - 1). - G. C. Greubel, Jan 05 2023

Edited and extended by Ray Chandler, Feb 07 2004

A096956 Pascal (1,6) triangle.

Original entry on oeis.org

6, 1, 6, 1, 7, 6, 1, 8, 13, 6, 1, 9, 21, 19, 6, 1, 10, 30, 40, 25, 6, 1, 11, 40, 70, 65, 31, 6, 1, 12, 51, 110, 135, 96, 37, 6, 1, 13, 63, 161, 245, 231, 133, 43, 6, 1, 14, 76, 224, 406, 476, 364, 176, 49, 6, 1, 15, 90, 300, 630, 882, 840, 540, 225, 55, 6, 1, 16, 105, 390, 930

Offset: 0

Wolfdieter Lang, Aug 13 2004

Except for the first row this is the row reversed (6,1)-Pascal triangle A093563.
This is the sixth member, q=6, in the family of (1,q) Pascal triangles: A007318 (Pascal (q=1)), A029635 (q=2) (but with a(0,0)=2, not 1), A095660 (q=3), A095666 (q=4), A096940 (q=5).
This is an example of a Riordan triangle (see A053121 for a comment and the 1991 Shapiro et al. reference on the Riordan group) with o.g.f. of column no. m of the type g(x)*(x*f(x))^m with f(0)=1. Therefore the o.g.f. for the row polynomials p(n,x):=Sum_{m=0..n} a(n,m)*x^m is G(z,x)=g(z)/(1-x*z*f(z)). Here: g(x)=(6-5*x)/(1-x), f(x)=1/(1-x), hence G(z,x)=(6-5*z)/(1-(1+x)*z).
The SW-NE diagonals give Sum_{k=0..ceiling((n-1)/2)} a(n-1-k,k) = A022097(n-2), n >= 2, with n=1 value 6. Observation by Paul Barry, Apr 29 2004. Proof via recursion relations and comparison of inputs.

			Triangle begins:
  [0]  6;
  [1]  1,  6;
  [2]  1,  7,  6;
  [3]  1,  8, 13,  6;
  [4]  1,  9, 21, 19,  6;
  [5]  1, 10, 30, 40, 25,  6;
  ...

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
Wolfdieter Lang, First 10 rows.

Row sums: A005009(n-1), n>=1, 6 if n=0; g.f.: (6-5*x)/(1-2*x). Alternating row sums are [6, -5, followed by 0's].

Column sequences (without leading zeros) give for m=1..9, with n >= 0: A000027(n+6), A056115, A096957-9, A097297-A097300.

a(n,k):=piecewise(n=0,6,0Mircea Merca, Apr 08 2012

A096956[n_, k_] := If[n == k, 6, (5*k/n + 1)*Binomial[n, k]];
Table[A096956[n, k], {n, 0, 12}, {k, 0, n}] (* Paolo Xausa, Apr 14 2025 *)

Recursion: a(n,m)=0 if m > n, a(0,0) = 6; a(n,0) = 1 if n >= 1; a(n,m) = a(n-1, m) + a(n-1, m-1).
G.f. column m (without leading zeros): (6-5*x)/(1-x)^(m+1), m >= 0.
a(n,k) = (1+5*k/n)*binomial(n,k), for n > 0. - Mircea Merca, Apr 08 2012

A336101 Numbers divisible by exactly one odd prime.

Original entry on oeis.org

3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 34, 36, 37, 38, 40, 41, 43, 44, 46, 47, 48, 49, 50, 52, 53, 54, 56, 58, 59, 61, 62, 67, 68, 71, 72, 73, 74, 76, 79, 80, 81, 82, 83, 86, 88, 89, 92, 94, 96, 97, 98, 100, 101, 103, 104

Offset: 1

Peter Munn, Jul 08 2020

Numbers k for which A001221(A000265(k)) = 1. - Antti Karttunen, Jul 08 2020
Numbers whose odd part is a prime power (A246655). - Amiram Eldar, Jul 08 2020
Numbers of the form 2^r * p^q  with p an odd prime (A065091), r >= 0, q >= 1. - Bernard Schott, Dec 14 2020

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000265, A001221, A246655, A340373 (characteristic function).
Positions of ones in A005087.
Subsequence of A267895.
Subsequences: A007283 (3*2^n), A020714 (5*2^n), A005009 (7*2^n), A005015 (11*2^n), A005029 (13*2^n), A038550 (p*2^n, p odd prime), A065091 (odd primes), A061345 \ {1} (odd prime powers).

Select[Range[104], PrimePowerQ[#/2^IntegerExponent[#, 2]] &] (* Amiram Eldar, Jul 08 2020 *)

isA336101(n) = (1==omega(n>>valuation(n,2))); \\ Antti Karttunen, Jul 08 2020

A081253 Numbers k such that A081252(m)/m^2 has a local minimum for m = k.

Original entry on oeis.org

2, 4, 9, 18, 37, 74, 149, 298, 597, 1194, 2389, 4778, 9557, 19114, 38229, 76458, 152917, 305834, 611669, 1223338, 2446677, 4893354, 9786709, 19573418, 39146837, 78293674, 156587349, 313174698, 626349397, 1252698794, 2505397589

Offset: 1

Klaus Brockhaus, Mar 17 2003

The limit of the local minima, lim_{n->infinity} A081252(n)/n^2 = 1/14. For local maxima cf. A081254.

			9 is a term since A081252(8)/8^2 = 5/64 = 0.078, A081252(9)/9^2 = 6/81 = 0.074, A081252(10)/10^2 = 8/100 = 0.080.

Michael De Vlieger, Table of n, a(n) for n = 1..3321
Klaus Brockhaus, Illustration for A053646, A081252, A081253 and A081254
Chris J. Mitchell and Peter R. Wild, Constructing orientable sequences, arXiv:2108.03069 [math.CO], 2021. See Table 2 p. 12 but with different offset.
Index entries for linear recurrences with constant coefficients, signature (2,1,-2).

Cf. A053646, A081252, A081254, A005009, A062092.

Cf. A266071 (binary).

Rest@ CoefficientList[Series[-x (x^2 - 2)/((x - 1) (x + 1) (2 x - 1)), {x, 0, 31}], x]

print([7*2**n//6 for n in range(1, 50)]) # Karl V. Keller, Jr., May 22 2022

a(n) = floor(2^(n-1)*7/3).
a(n) = a(n-2) + 7*2^(n-3) for n > 2; a(n+2) - a(n) = A005009(n-1); a(n+1) - a(n) = A062092(n-1).
G.f.: -x*(x^2 - 2)/((x - 1)*(x + 1)*(2*x - 1)).
a(n) = 2*a(n-1) for even n, otherwise a(n) = 2*a(n-1)+1, with a(1)=2. - Bruno Berselli, Jun 19 2014

Formulas adjusted to be consistent with offset 1 by Pontus von Brömssen, Sep 27 2021

A048489 a(n) = 7 * 2^n - 6.

Original entry on oeis.org

1, 8, 22, 50, 106, 218, 442, 890, 1786, 3578, 7162, 14330, 28666, 57338, 114682, 229370, 458746, 917498, 1835002, 3670010, 7340026, 14680058, 29360122, 58720250, 117440506, 234881018, 469762042, 939524090, 1879048186

Offset: 0

Clark Kimberling

Number of 3 X n 0-1 matrices avoiding simultaneously the right angled numbered polyomino patterns (ranpp) (00;1), (10;0) and (11;0). An occurrence of a ranpp (xy;z) in a matrix A=(a(i,j)) is a triple (a(i1,j1), a(i1,j2), a(i2,j1)) where i1Sergey Kitev, Nov 13 2004
Row sums of triangle A131115. - N. J. A. Sloane, Nov 10 2007
Equals binomial transform of [1, 7, 7, 7, ...]. - Gary W. Adamson, Apr 28 2008
Number of variations of a Componium barrel which produces n phrases. This sequence describes the variations produced by the Componium, a historical mechanical organ. Another way of describing it is: Number of base 8 n-digit numbers produced by repeating or advancing along this 14-step cycle: (0,1,2,3,4,5,6,7,6,5,4,3,2,1). Subset of A126362. - Jim Bumgardner, Dec 10 2013
a(n) = the sum of the terms in row(n) in a triangle with first column T(n,0)=
1+2*n and diagonal T(n,n)=1+4*n with T(i,j)=T(i-1,j-1) + T(i-1,j). - J. M. Bergot, May 11 2018

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Jim Bumgardner, Variations of the Componium, 2013
S. Kitaev, On multi-avoidance of right angled numbered polyomino patterns, Integers: Electronic Journal of Combinatorial Number Theory 4 (2004), A21, 20pp.
Index entries for linear recurrences with constant coefficients, signature (3,-2).

a(n)=T(6, n), array T given by A048483.
n-th difference of a(n), a(n-1), ..., a(0) is (7, 7, 7, ...).
Cf. A131115.

A048489:=n->7*2^n-6: seq(A048489(n), n=0..40); # Wesley Ivan Hurt, Apr 18 2017

CoefficientList[Series[(1 + 5 x)/((2 x - 1) (x - 1)), {x, 0, 28}], x] (* Michael De Vlieger, May 22 2018 *)
7*2^Range[0,30]-6 (* or *) LinearRecurrence[{3,-2},{1,8},30] (* Harvey P. Dale, May 19 2019 *)

a(n)=7<Charles R Greathouse IV, Dec 10 2013

a(n) = A000079(n)*7-6 = A005009(n)-6. - Omar E. Pol, Dec 21 2008
a(n) = 2*a(n-1)+6 with n>0, a(0)=1. - Vincenzo Librandi, Aug 06 2010
G.f.: ( 1+5*x ) / ( (2*x-1)*(x-1) ). - R. J. Mathar, Oct 21 2012
a(n) = A063757(2*n). - Philippe Deléham, Apr 13 2013

A110287 a(n) = 17*2^n.

Original entry on oeis.org

17, 34, 68, 136, 272, 544, 1088, 2176, 4352, 8704, 17408, 34816, 69632, 139264, 278528, 557056, 1114112, 2228224, 4456448, 8912896, 17825792, 35651584, 71303168, 142606336, 285212672, 570425344, 1140850688, 2281701376, 4563402752, 9126805504, 18253611008

Offset: 0

Alexandre Wajnberg, Sep 07 2005

The first differences are the sequence itself. Doubling the terms gives the same sequence (beginning one step further).

17 times powers of 2. - Omar E. Pol, Dec 17 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..235
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2).

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A003945 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), this sequence (m=8), A110288 (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).

Cf. A007283.

[17*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

17*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
NestList[2#&,17,30] (* Harvey P. Dale, Jul 21 2014 *)

a(n)=17*2^n \\ Charles R Greathouse IV, Oct 07 2015

[17*2^n for n in range(51)] # G. C. Greubel, Jan 05 2023

G.f.: 17/(1-2*x). - Philippe Deléham, Nov 23 2008
a(n) = 17*A000079(n). - Omar E. Pol, Dec 17 2008
a(n) = 2*a(n-1) (with a(0)=17). - Vincenzo Librandi, Dec 26 2010
a(n) = A173786(n+4, n) for n>3. - Reinhard Zumkeller, Feb 28 2010
E.g.f.: 17*exp(2*x). - G. C. Greubel, Jan 05 2023

Edited by Omar E. Pol, Dec 16 2008

A168230 a(n) = n + 2 - a(n-1) for n>1; a(1) = 0.

Original entry on oeis.org

0, 4, 1, 5, 2, 6, 3, 7, 4, 8, 5, 9, 6, 10, 7, 11, 8, 12, 9, 13, 10, 14, 11, 15, 12, 16, 13, 17, 14, 18, 15, 19, 16, 20, 17, 21, 18, 22, 19, 23, 20, 24, 21, 25, 22, 26, 23, 27, 24, 28, 25, 29, 26, 30, 27, 31, 28, 32, 29, 33, 30, 34, 31, 35, 32, 36, 33, 37, 34, 38, 35, 39, 36, 40, 37

Offset: 1

Vincenzo Librandi, Nov 21 2009

Interleaving of A001477 and A000027 without first three terms.
Binomial transform of 0, 4 followed by a signed version of A005009.
Inverse binomial transform of A034007 without first and third term.

			a(2) = 2+2-a(1) = 4-0 = 4; a(3) = 3+2-a(2) = 5-4 = 1.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A001477 (nonnegative integers), A000027 (positive integers), A168309 (repeat 4,-3), A005009 (7*2^n), A034007 (first differences of A045891).

[ n eq 1 select 0 else -Self(n-1)+n+2: n in [1..75] ];

a=3; Table[a=n-a, {n, 3, 200}] (* Vladimir Joseph Stephan Orlovsky, Nov 22 2009 *)
CoefficientList[Series[x (4 - 3 x) / ((1 + x) (1 - x)^2),{x, 0, 100}], x] (* Vincenzo Librandi, Sep 16 2013 *)
LinearRecurrence[{1,1,-1}, {0, 4, 1}, 50] (* G. C. Greubel, Jul 16 2016 *)
nxt[{n_,a_}]:={n+1,n+3-a}; NestList[nxt,{1,0},80][[All,2]] (* Harvey P. Dale, May 28 2021 *)

Vec(x^2*(4-3*x)/((1+x)*(1-x)^2) + O(x^100)) \\ Colin Barker, Nov 08 2014

G.f.: x^2*(4 - 3*x)/((1+x)*(1-x)^2).
a(n) = (7*(-1)^n + 2*n + 5)/4.
a(n) = a(n-2) + 1 for n>2; a(1)=0, a(2)=4.
a(n+1) - a(n) = A168309(n).
a(n) = a(n-1) + a(n-2) - a(n-3). - Colin Barker, Nov 08 2014
E.g.f.: (1/4)*(7 - 12*exp(x) + (5 + 2*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016
Sum_{n>=2} (-1)^(n+1)/a(n) = 11/6. - Amiram Eldar, Feb 23 2023

Edited, three comments, four formulas, MAGMA program added by Klaus Brockhaus, Nov 22 2009

A237930 a(n) = 3^(n+1) + (3^n-1)/2.

Original entry on oeis.org

3, 10, 31, 94, 283, 850, 2551, 7654, 22963, 68890, 206671, 620014, 1860043, 5580130, 16740391, 50221174, 150663523, 451990570, 1355971711, 4067915134, 12203745403, 36611236210, 109833708631, 329501125894, 988503377683, 2965510133050, 8896530399151

Offset: 0

Philippe Deléham, Feb 16 2014

a(n-1) agrees with the graph radius of the n-Sierpinski carpet graph for n = 2 to at least n = 5. See A100774 for the graph diameter of the n-Sierpinski carpet graph.
The inverse binomial transform gives 3, 7, 14, 28, 56, ... i.e., A005009 with a leading 3. - R. J. Mathar, Jan 08 2020
First differences of A108765. The digital root of a(n) for n > 1 is always 4. a(n) is never divisible by 7 or by 12. a(n) == 10 (mod 84) for odd n. a(n) == 31 (mod 84) for even n > 0. Conjecture: This sequence contains no prime factors p == {11, 13, 23, 61 71, 73} (mod 84). - Klaus Purath, Apr 13 2020
This is a subsequence of A017209 for n > 1. See formula. - Klaus Purath, Jul 03 2020

			Ternary....................Decimal
10...............................3
101.............................10
1011............................31
10111...........................94
101111.........................283
1011111........................850
10111111......................2551
101111111.....................7654, etc.

Colin Barker, Table of n, a(n) for n = 0..1000
Eric Weisstein's World of Mathematics, Graph Radius.
Eric Weisstein's World of Mathematics, Sierpinski Carpet Graph.
Index entries for linear recurrences with constant coefficients, signature (4,-3).

Cf. A000244, A003462, A005009, A005032 (first differences), A017209, A060816, A100774, A108765 (partial sums), A199109, A329774.

Cf. A024023, A029858, A057198, A116952, A171498.

[3^(n+1) + (3^n-1)/2: n in [0..40]]; // Vincenzo Librandi, Jan 09 2020

(* Start from Eric W. Weisstein, Mar 13 2018 *)
Table[(7 3^n - 1)/2, {n, 0, 20}]
(7 3^Range[0, 20] - 1)/2
LinearRecurrence[{4, -3}, {10, 31}, {0, 20}]
CoefficientList[Series[(3 - 2 x)/((x - 1) (3 x - 1)), {x, 0, 20}], x]
(* End *)

Vec((3 - 2*x) / ((1 - x)*(1 - 3*x)) + O(x^30)) \\ Colin Barker, Nov 27 2019

G.f.: (3-2*x)/((1-x)*(1-3*x)).
a(n) = A000244(n+1) + A003462(n).
a(n) = 3*a(n-1) + 1 for n > 0, a(0)=3. (Note that if a(0) were 1 in this recurrence we would get A003462, if it were 2 we would get A060816. - N. J. A. Sloane, Dec 06 2019)
a(n) = 4*a(n-1) - 3*a(n-2) for n > 1, a(0)=3, a(1)=10.
a(n) = 2*a(n-1) + 3*a(n-2) + 2 for n > 1.
a(n) = A199109(n) - 1.
a(n) = (7*3^n - 1)/2. - Eric W. Weisstein, Mar 13 2018
From Klaus Purath, Apr 13 2020: (Start)
a(n) = A057198(n+1) + A024023(n).
a(n) = A029858(n+2) - A024023(n).
a(n) = A052919(n+1) + A029858(n+1).
a(n) = (A000244(n+1) + A171498(n))/2.
a(n) = 7*A003462(n) + 3.
a(n) = A116952(n) + 2. (End)
a(n) = A017209(7*(3^(n-2)-1)/2 + 3), n > 1. - Klaus Purath, Jul 03 2020
E.g.f.: exp(x)*(7*exp(2*x) - 1)/2. - Stefano Spezia, Aug 28 2023

A047352 Numbers that are congruent to {0, 2} mod 7.

Original entry on oeis.org

0, 2, 7, 9, 14, 16, 21, 23, 28, 30, 35, 37, 42, 44, 49, 51, 56, 58, 63, 65, 70, 72, 77, 79, 84, 86, 91, 93, 98, 100, 105, 107, 112, 114, 119, 121, 126, 128, 133, 135, 140, 142, 147, 149, 154, 156, 161, 163, 168, 170

Offset: 1

N. J. A. Sloane

Numbers k such that k^2/7 + k*(k + 1)/14 = k*(3*k + 1)/14 is a nonnegative integer. - Bruno Berselli, Feb 14 2017

David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Cf. A005009, A030308.

LinearRecurrence[{1,1,-1},{0,2,7},50] (* Harvey P. Dale, Oct 16 2022 *)

forstep(n=0,200,[2,5],print1(n", ")) \\ Charles R Greathouse IV, Oct 17 2011

a(n) = 7*n - a(n-1) - 12 with a(1)=0. Also: a(n) = a(n-1) + a(n-2) - a(n-3). - Vincenzo Librandi, Aug 05 2010
a(n+1) = Sum_{k>=0} A030308(n,k)*b(k) with b(0)=2 and b(k)=A005009(k-1) for k>0. - Philippe Deléham, Oct 17 2011
G.f.: x^2*(2 + 5*x)/((1 + x)*(1 - x)^2). - R. J. Mathar, Dec 04 2011
a(n) = floor((7/3)*floor(3*n/2)). - Clark Kimberling, Jul 04 2012
E.g.f.: 5 + ((14*x - 17)*exp(x) - 3*exp(-x))/4. - David Lovler, Aug 31 2022

A110288 a(n) = 19*2^n.

Original entry on oeis.org

19, 38, 76, 152, 304, 608, 1216, 2432, 4864, 9728, 19456, 38912, 77824, 155648, 311296, 622592, 1245184, 2490368, 4980736, 9961472, 19922944, 39845888, 79691776, 159383552, 318767104, 637534208, 1275068416, 2550136832, 5100273664, 10200547328, 20401094656

Offset: 0

Alexandre Wajnberg, Sep 07 2005

The first differences are the sequence itself. Doubling the terms gives the same sequence (beginning one step further).

19 times powers of 2. - Omar E. Pol, Dec 17 2008

Vincenzo Librandi, Table of n, a(n) for n = 0..235
Tanya Khovanova, Recursive Sequences
Index entries for linear recurrences with constant coefficients, signature (2).

Sequences of the form (2*m+1)*2^n: A000079 (m=0), A007283 (m=1), A020714 (m=2), A005009 (m=3), A005010 (m=4), A005015 (m=5), A005029 (m=6), A110286 (m=7), A110287 (m=8), this sequence (m=9), A175805 (m=10), A248646 (m=11), A164161 (m=12), A175806 (m=13), A257548 (m=15).

[19*2^n: n in [0..40]]; // Vincenzo Librandi, Apr 28 2011

19*2^Range[0, 60] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
NestList[2#&,19,30] (* Harvey P. Dale, May 11 2018 *)

[19*2^n for n in range(41)] # G. C. Greubel, Jan 04 2023

G.f.: 19/(1-2*x). - Philippe Deléham, Nov 23 2008
a(n) = A000079(n)*19. - Omar E. Pol, Dec 17 2008
E.g.f.: 19*exp(2*x). - G. C. Greubel, Jan 04 2023

Edited by Omar E. Pol, Dec 16 2008

cp's OEIS Frontend

A091629 Product of digits associated with A091628(n). Essentially the same as A007283.

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A096956 Pascal (1,6) triangle.

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A336101 Numbers divisible by exactly one odd prime.

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A081253 Numbers k such that A081252(m)/m^2 has a local minimum for m = k.

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A048489 a(n) = 7 * 2^n - 6.

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A110287 a(n) = 17*2^n.

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A168230 a(n) = n + 2 - a(n-1) for n>1; a(1) = 0.

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