A017173 -id:A017173 - cp's OEIS frontend

A354939 Row 9 of A354940: Numbers k for which A345992(k) = 9, divided by 9.

5, 7, 10, 14, 16, 19, 23, 25, 28, 32, 37, 41, 43, 46, 50, 59, 61, 64, 68, 73, 79, 82, 86, 91, 97, 100, 109, 113, 118, 122, 127, 131, 136, 145, 149, 151, 158, 163, 167, 169, 172, 181, 185, 194, 199, 212, 221, 223, 226, 235, 239, 241, 244, 253, 257, 262, 271, 277, 289, 293, 298, 302, 307, 311, 313, 316, 325, 331, 334

Offset: 1

Antti Karttunen, Jun 15 2022

nonn

Apparently, all terms are either of the form 9k+1 (in A017173), or 9k+5 (in A017221), or 9k+7 (in A017245).

Row 9 of A354940.

Cf. A017173, A017221, A017245, A344005, A345992.

q[n_] := Module[{m = 1}, While[!Divisible[m*(m + 1), 9*n], m++]; GCD[9*n, m] == 9]; Select[Range[335], q] (* Amiram Eldar, Jun 17 2022 *)

A354939(n) = A354940sq(9,n); \\ See the program in A354940.

A001534 a(n) = (9n+1)(9*n+8).

Original entry on oeis.org

8, 170, 494, 980, 1628, 2438, 3410, 4544, 5840, 7298, 8918, 10700, 12644, 14750, 17018, 19448, 22040, 24794, 27710, 30788, 34028, 37430, 40994, 44720, 48608, 52658, 56870, 61244, 65780, 70478, 75338, 80360, 85544, 90890, 96398, 102068, 107900, 113894, 120050

Offset: 0

N. J. A. Sloane

T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A017173, A017257.

f[n_]:=Module[{n9=9n},(n9+1)(n9+8)];Array[f,40,0] (* or *) LinearRecurrence[ {3,-3,1},{8,170,494},50] (* Harvey P. Dale, Aug 20 2011 *)

a(n)=(9*n+1)*(9*n+8) \\ Charles R Greathouse IV, Jun 17 2017

a(n) = 162*n + a(n-1) with a(0)=8. - Vincenzo Librandi, Nov 12 2010
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0)=8, a(1)=170, a(2)=494. - Harvey P. Dale, Aug 20 2011
G.f.: -((2*(x*(4*x+73)+4))/(x-1)^3). - Harvey P. Dale, Aug 20 2011
Sum_{n>=0} 1/a(n) = (Psi(8/9)-Psi(1/9))/63 = 0.13700722.. - R. J. Mathar, May 30 2022
Sum_{n>=0} 1/a(n) = cot(Pi/9)*Pi/63. - Amiram Eldar, Sep 10 2022
From Amiram Eldar, Feb 19 2023: (Start)
a(n) = A017173(n)*A017257(n).
Product_{n>=0} (1 - 1/a(n)) = cosec(Pi/9)*cos(sqrt(53)*Pi/18).
Product_{n>=0} (1 + 1/a(n)) = cosec(Pi/9)*cos(sqrt(5)*Pi/6). (End)
E.g.f.: exp(x)*(8 + 81*x*(2 + x)). - Elmo R. Oliveira, Oct 18 2024

A115282 Correlation triangle for the sequence 3-2*0^n.

Original entry on oeis.org

1, 3, 3, 3, 10, 3, 3, 12, 12, 3, 3, 12, 19, 12, 3, 3, 12, 21, 21, 12, 3, 3, 12, 21, 28, 21, 12, 3, 3, 12, 21, 30, 30, 21, 12, 3, 3, 12, 21, 30, 37, 30, 21, 12, 3, 3, 12, 21, 30, 39, 39, 30, 21, 12, 3, 3, 12, 21, 30, 39, 46, 39, 30, 21, 12, 3

Offset: 0

Paul Barry, Jan 19 2006

Row sums are A102214. Diagonal sums are A115283. T(2n,n) is 9n+1 (A017173), the partial sums of (3-2*0^n)^2. T(2n,n)-T(2n,n+1) is 7-6*0^n.

			Triangle begins
1;
3, 3;
3,10, 3;
3,12,12, 3;
3,12,19,12, 3;
3,12,21,21,12, 3;
3,12,21,28,21,12,3;

G.f.: (1+2x)(1+2x*y)/((1-x)(1-x*y)(1-x^2*y)); Number triangle T(n, k)=sum{j=0..n, [j<=k]*(3-2*0^(k-j))*[j<=n-k]*(3-2*0^(n-k-j))}.

A141324 Sum of digits of A002452(n).

Original entry on oeis.org

0, 1, 1, 10, 10, 19, 19, 37, 28, 37, 37, 37, 37, 46, 73, 55, 55, 64, 73, 73, 64, 82, 73, 109, 100, 118, 91, 109, 109, 118, 127, 127, 109, 136, 145, 127, 145, 136, 145, 163, 145, 154, 172, 190, 127, 181, 199, 208, 217, 190, 181, 235, 235, 253, 226, 217, 226, 235, 262

Offset: 0

Paul Curtz, Aug 03 2008

Cf. A017173.

A002452 := proc(n) (9^n-1)/8 ; end: A007953 := proc(n) local i ; add(i,i=convert(n,base,10)) ; end: A141324 := proc(n) A007953(A002452(n)) ; end: for n from 0 to 80 do printf("%d,",A141324(n)) ; od: # R. J. Mathar, Aug 09 2008

Total[IntegerDigits[#]]&/@LinearRecurrence[{10,-9},{0,1},60] (* Harvey P. Dale, Sep 23 2018 *)

a(n)=A007953(A002452(n)).

Extended by R. J. Mathar, Aug 09 2008

A168416 a(n) = 1 + 9*floor(n/2).

Original entry on oeis.org

1, 10, 10, 19, 19, 28, 28, 37, 37, 46, 46, 55, 55, 64, 64, 73, 73, 82, 82, 91, 91, 100, 100, 109, 109, 118, 118, 127, 127, 136, 136, 145, 145, 154, 154, 163, 163, 172, 172, 181, 181, 190, 190, 199, 199, 208, 208, 217, 217, 226, 226, 235, 235, 244, 244, 253, 253

Offset: 1

Vincenzo Librandi, Nov 25 2009

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

Cf. A017173.

[1+9*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 19 2013

Table[1 + 9 Floor[n/2], {n, 70}] (* or *) CoefficientList[Series[(1 + 9 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 19 2013 *)

a(n) = 9*n - a(n-1) - 7, with n>1, a(1)=1.
G.f.: x*(1 + 9*x - x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 19 2013
a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 19 2013
E.g.f.: (1/4)*(9 - 4*exp(x) + (18*x - 5)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 22 2016

New definition by Vincenzo Librandi, Sep 19 2013

A172174 a(n) = 90*a(n-1) + 1.

Original entry on oeis.org

1, 91, 8191, 737191, 66347191, 5971247191, 537412247191, 48367102247191, 4353039202247191, 391773528202247191, 35259617538202247191, 3173365578438202247191, 285602902059438202247191, 25704261185349438202247191, 2313383506681449438202247191

Offset: 1

Mark Dols, Jan 28 2010

Difference of pairs of integers given in A162849.

Sum of digits give A017173.

Colin Barker, Table of n, a(n) for n = 1..512
Index entries for linear recurrences with constant coefficients, signature (91,-90).

Cf. A017173, A162849, A165154.

NestList[90#+1&,1,20] (* Harvey P. Dale, Aug 29 2014 *)

Vec(1/((x-1)*(90*x-1)) + O(x^30)) \\ Colin Barker, Oct 02 2015

[(90^n -1)/89 for n in (1..50)] # G. C. Greubel, Apr 26 2022

From Colin Barker, Oct 02 2015: (Start)
a(n) = 91*a(n-1) - 90*a(n-2) for n>2.
G.f.: 1 / ((1-x)*(1-90*x)). (End)

A231233 Triangle T(n,k) = greatest prime factor of n*k+1.

Original entry on oeis.org

2, 3, 5, 2, 7, 5, 5, 3, 13, 17, 3, 11, 2, 7, 13, 7, 13, 19, 5, 31, 37, 2, 5, 11, 29, 3, 43, 5, 3, 17, 5, 11, 41, 7, 19, 13, 5, 19, 7, 37, 23, 11, 2, 73, 41, 11, 7, 31, 41, 17, 61, 71, 3, 13, 101, 3, 23, 17, 5, 7, 67, 13, 89, 5, 37, 61, 13, 5, 37, 7, 61, 73, 17, 97, 109, 11, 19, 29

Offset: 1

Michel Marcus, Nov 06 2013

			Triangle begins:
  2;
  3,  5;
  2,  7,  5;
  5,  3, 13, 17;
  3, 11,  2,  7, 13;
  7, 13, 19,  5, 31, 37;
  2,  5, 11, 29,  3, 43,  5;

Michel Marcus, Rows n = 1..100 of triangle, flattened
Étienne Fouvry, On the greatest prime factor of ab+1, arXiv:1311.1161 [math.NT], 2013.

Cf. A005408, A016777, A016813, A016861, A016921, A016993, A017077, A017173.

Flat(List([1..12],n->List([1..n],k->Maximum(FactorsInt(n*k+1))))); # Muniru A Asiru, Sep 23 2018

T[n_, k_] := FactorInteger[n k + 1][[-1, 1]];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Sep 23 2018 *)

tabl(nn) = {for (n=1, nn, for (k=1, n, f = factor(n*k+1); print1(f[#f~, 1], ", ");); print(););}

T(n, k) = A006530(n*k+1).

A296180 Triangle read by rows: T(n, k) = 3(n - k)k + 1, n >= 0, 0 <= k <= n.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 10, 13, 10, 1, 1, 13, 19, 19, 13, 1, 1, 16, 25, 28, 25, 16, 1, 1, 19, 31, 37, 37, 31, 19, 1, 1, 22, 37, 46, 49, 46, 37, 22, 1, 1, 25, 43, 55, 61, 61, 55, 43, 25, 1, 1, 28, 49, 64, 73, 76, 73, 64, 49, 28, 1

Offset: 0

Wolfdieter Lang, Dec 20 2017

This is member m = 3 of the family of triangles T(m; n, k) = m*(n - k)*k + 1, for m >= 0. For m = 0: A000012(n, k) (read as a triangle); for m = 1: A077028 (rascal), for m = 2: T(2, n+1, k+1) = A130154(n, k). Motivated by A130154 to look at this family of triangles.
In general the recurrence is: T(m; n, 0) = 1 and T(m; n, n) = 1 for n >= 0; T(m; n, k) = (T(m; n-1, k-1)*T(m; n-1, k) + m)/T(m; n-2, k-1), for n >= 2, k = 1..n-1.
The general g.f. of the sequence of column k (with leading zeros) is G(m; k, x) = (x^k/(1 - x)^2)*(1 + (m*k - 1)*x), k >= 0.
The general g.f. of the triangle T(m;, n, k) is GT(m; x, t) = (1 - (1 + t)*x + (m+1)*t*x^2)/((1 - t*x)*(1 - x))^2, and G(m; k, x) = (d/dt)^k GT(m; x, t)/k!|_{t=0}.
For a simple combinatorial interpretation see the one given in A130154 by Rogério Serôdio which can be generalized to m >= 3.

			The triangle T(n, k) begins:
n\k   0  1  2  3  4  5  6  7  8  9 10 ...
0:    1
1:    1  1
2:    1  4  1
3:    1  7  7  1
4:    1 10 13 10  1
5:    1 13 19 19 13  1
6:    1 16 25 28 25 16  1
7:    1 19 31 37 37 31 19  1
8:    1 22 37 46 49 46 37 22  1
9:    1 25 43 55 61 61 55 43 25  1
10:   1 28 49 64 73 76 73 64 49 28  1
...
Recurrence: 28 = T(6, 3) = (19*19 + 3)/13 = 28.

Cf. A077028, A130154.

Columns (without leading zeros): A000012, A016777, A016921, A016921, A017173, A017533, ...

Table[3 k (n - k) + 1, {n, 0, 10}, {k, 0, n}] // Flatten (* Michael De Vlieger, Dec 20 2017 *)

lista(nn) = for(n=0, nn, for(k=0, n, print1(3*(n - k)*k + 1, ", "))) \\ Iain Fox, Dec 21 2017

T(n, k) = 3*(n - k)*k + 1, n >= 0, 0 <= k <= n,
Recurrence: T(n, 0) = 1 and T(n, n) = 1 for n >= 0; T(n, k) = (T(n-1, k-1)*T(n-1, k) + 3)/T(n-2, k-1), for n >= 2, k = 1..n-1.
G.f. of column k (with leading zeros): (x^k/(1 - x)^2)*(1 + (3*k-1)*x), k >= 0.
G.f. of triangle: (1 - (1 + t)*x + 4*t*x^2)/((1 - t*x)*(1 - x))^2 = 1 + (1+t)*x +(1 + 4*t + t^2)*x^2 + (1 + 7*t + 7*t^2 + t^3)*x^3 = ...

A301617 Numbers not divisible by 2, 3 or 5 (A007775) with digital root 1.

Original entry on oeis.org

1, 19, 37, 73, 91, 109, 127, 163, 181, 199, 217, 253, 271, 289, 307, 343, 361, 379, 397, 433, 451, 469, 487, 523, 541, 559, 577, 613, 631, 649, 667, 703, 721, 739, 757, 793, 811, 829, 847, 883, 901, 919, 937, 973, 991, 1009, 1027, 1063, 1081, 1099

Offset: 1

Gary Croft, Mar 24 2018

Numbers == {1, 19, 37, 73} mod 90 with additive sum sequence 1{+18+18+36+18} {repeat ...}. Includes all prime numbers > 7 with digital root 1.

			1+18=19; 19+18=37; 37+36=73; 73+18=91; 91+18=109.

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

Cf. A177704, A045572.

Intersection of A007775 and A017173.

seq(seq(i+90*j,i=[1,19,37,73]),j=0..30); # Robert Israel, Mar 25 2018

LinearRecurrence[{1,0,0,1,-1},{1,19,37,73,91},50] (* Harvey P. Dale, Dec 14 2019 *)

a(n) = 1 + 18 * (n - 1 + n\4) \\ David A. Corneth, Mar 24 2018

Vec(x*(1 + 18*x + 18*x^2 + 36*x^3 + 17*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Mar 24 2018

n == {1, 19, 37, 73} mod 90.
a(n + 1) = a(n) + 18 * A177704(n + 1). - David A. Corneth, Mar 24 2018
From Colin Barker, Mar 24 2018: (Start)
G.f.: x*(1 + 18*x + 18*x^2 + 36*x^3 + 17*x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.
(End)

The missing term 1081 added to the sequence by Colin Barker, Mar 24 2018

A303273 Array T(n,k) = binomial(n, 2) + k*n + 1 read by antidiagonals.

Original entry on oeis.org

1, 1, 1, 1, 2, 2, 1, 3, 4, 4, 1, 4, 6, 7, 7, 1, 5, 8, 10, 11, 11, 1, 6, 10, 13, 15, 16, 16, 1, 7, 12, 16, 19, 21, 22, 22, 1, 8, 14, 19, 23, 26, 28, 29, 29, 1, 9, 16, 22, 27, 31, 34, 36, 37, 37, 1, 10, 18, 25, 31, 36, 40, 43, 45, 46, 46, 1, 11, 20, 28, 35, 41

Offset: 0

Franck Maminirina Ramaharo, Apr 20 2018

Columns are linear recurrence sequences with signature (3,-3,1).
8*T(n,k) + A166147(k-1) are squares.
Columns k are binomial transforms of [1, k, 1, 0, 0, 0, ...].
Antidiagonals sums yield A116731.

			The array T(n,k) begins
1    1    1    1    1    1    1    1    1    1    1    1    1  ...  A000012
1    2    3    4    5    6    7    8    9   10   11   12   13  ...  A000027
2    4    6    8   10   12   14   16   18   20   22   24   26  ...  A005843
4    7   10   13   16   19   22   25   28   31   34   37   40  ...  A016777
7   11   15   19   23   27   31   35   39   43   47   51   55  ...  A004767
11  16   21   26   31   36   41   46   51   56   61   66   71  ...  A016861
16  22   28   34   40   46   52   58   64   70   76   82   88  ...  A016957
22  29   36   43   50   57   64   71   78   85   92   99  106  ...  A016993
29  37   45   53   61   69   77   85   93  101  109  117  125  ...  A004770
37  46   55   64   73   82   91  100  109  118  127  136  145  ...  A017173
46  56   66   76   86   96  106  116  126  136  146  156  166  ...  A017341
56  67   78   89  100  111  122  133  144  155  166  177  188  ...  A017401
67  79   91  103  115  127  139  151  163  175  187  199  211  ...  A017605
79  92  105  118  131  144  157  170  183  196  209  222  235  ...  A190991
...
The inverse binomial transforms of the columns are
1    1    1    1    1    1    1    1    1    1    1    1    1  ...
0    1    2    3    4    5    6    7    8    9   10   11   12  ...
1    1    1    1    1    1    1    1    1    1    1    1    1  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
0    0    0    0    0    0    0    0    0    0    0    0    0  ...
...
T(k,n-k) = A087401(n,k) + 1 as triangle
1
1   1
1   2   2
1   3   4   4
1   4   6   7   7
1   5   8  10  11  11
1   6  10  13  15  16  16
1   7  12  16  19  21  22  22
1   8  14  19  23  26  28  29  29
1   9  16  22  27  31  34  36  37  37
1  10  18  25  31  36  40  43  45  46  46
...

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics: A Foundation for Computer Science, Addison-Wesley, 1994.

Cf. A085475, A086270, A086271, A086272, A086273, A130154, A159798, A162609, A162610, A300401.

T := (n, k) -> binomial(n, 2) + k*n + 1;
for n from 0 to 20 do seq(T(n, k), k = 0 .. 20) od;

Table[With[{n = m - k}, Binomial[n, 2] + k n + 1], {m, 0, 11}, {k, m, 0, -1}] // Flatten (* Michael De Vlieger, Apr 21 2018 *)

T(n, k) := binomial(n, 2)+ k*n + 1$
for n:0 thru 20 do
    print(makelist(T(n, k), k, 0, 20));

T(n,k) = binomial(n, 2) + k*n + 1;
tabl(nn) = for (n=0, nn, for (k=0, nn, print1(T(n, k), ", ")); print); \\ Michel Marcus, May 17 2018

G.f.: (3*x^2*y - 3*x*y + y - 2*x^2 + 2*x - 1)/((x - 1)^3*(y - 1)^2).
E.g.f.: (1/2)*(2*x*y + x^2 + 2)*exp(y + x).
T(n,k) = 3*T(n-1,k) - 3*T(n-2,k) + T(n-3,k), with T(0,k) = 1, T(1,k) = k + 1 and T(2,k) = 2*k + 2.
T(n,k) = T(n-1,k) + n + k - 1.
T(n,k) = T(n,k-1) + n, with T(n,0) = 1.
T(n,0) = A152947(n+1).
T(n,1) = A000124(n).
T(n,2) = A000217(n).
T(n,3) = A034856(n+1).
T(n,4) = A052905(n).
T(n,5) = A051936(n+4).
T(n,6) = A246172(n+1).
T(n,7) = A302537(n).
T(n,8) = A056121(n+1) + 1.
T(n,9) = A056126(n+1) + 1.
T(n,10) = A051942(n+10) + 1, n > 0.
T(n,11) = A101859(n) + 1.
T(n,12) = A132754(n+1) + 1.
T(n,13) = A132755(n+1) + 1.
T(n,14) = A132756(n+1) + 1.
T(n,15) = A132757(n+1) + 1.
T(n,16) = A132758(n+1) + 1.
T(n,17) = A212427(n+1) + 1.
T(n,18) = A212428(n+1) + 1.
T(n,n) = A143689(n) = A300192(n,2).
T(n,n+1) = A104249(n).
T(n,n+2) = T(n+1,n) = A005448(n+1).
T(n,n+3) = A000326(n+1).
T(n,n+4) = A095794(n+1).
T(n,n+5) = A133694(n+1).
T(n+2,n) = A005449(n+1).
T(n+3,n) = A115067(n+2).
T(n+4,n) = A133694(n+2).
T(2*n,n) = A054556(n+1).
T(2*n,n+1) = A054567(n+1).
T(2*n,n+2) = A033951(n).
T(2*n,n+3) = A001107(n+1).
T(2*n,n+4) = A186353(4*n+1) (conjectured).
T(2*n,n+5) = A184103(8*n+1) (conjectured).
T(2*n,n+6) = A250657(n-1) = A250656(3,n-1), n > 1.
T(n,2*n) = A140066(n+1).
T(n+1,2*n) = A005891(n).
T(n+2,2*n) = A249013(5*n+4) (conjectured).
T(n+3,2*n) = A186384(5*n+3) = A186386(5*n+3) (conjectured).
T(2*n,2*n) = A143689(2*n).
T(2*n+1,2*n+1) = A143689(2*n+1) (= A030503(3*n+3) (conjectured)).
T(2*n,2*n+1) = A104249(2*n) = A093918(2*n+2) = A131355(4*n+1) (= A030503(3*n+5) (conjectured)).
T(2*n+1,2*n) = A085473(n).
a(n+1,5*n+1)=A051865(n+1) + 1.
a(n,2*n+1) = A116668(n).
a(2*n+1,n) = A054569(n+1).
T(3*n,n) = A025742(3*n-1), n > 1 (conjectured).
T(n,3*n) = A140063(n+1).
T(n+1,3*n) = A069099(n+1).
T(n,4*n) = A276819(n).
T(4*n,n) = A154106(n-1), n > 0.
T(2^n,2) = A028401(n+2).
T(1,n)*T(n,1) = A006000(n).
T(n*(n+1),n) = A211905(n+1), n > 0 (conjectured).
T(n*(n+1)+1,n) = A294259(n+1).
T(n,n^2+1) = A081423(n).
T(n,A000217(n)) = A158842(n), n > 0.
T(n,A152947(n+1)) = A060354(n+1).
floor(T(n,n/2)) = A267682(n) (conjectured).
floor(T(n,n/3)) = A025742(n-1), n > 0 (conjectured).
floor(T(n,n/4)) = A263807(n-1), n > 0 (conjectured).
ceiling(T(n,2^n)/n) = A134522(n), n > 0 (conjectured).
ceiling(T(n,n/2+n)/n) = A051755(n+1) (conjectured).
floor(T(n,n)/n) = A133223(n), n > 0 (conjectured).
ceiling(T(n,n)/n) = A007494(n), n > 0.
ceiling(T(n,n^2)/n) = A171769(n), n > 0.
ceiling(T(2*n,n^2)/n) = A046092(n), n > 0.
ceiling(T(2*n,2^n)/n) = A131520(n+2), n > 0.

cp's OEIS Frontend

A354939 Row 9 of A354940: Numbers k for which A345992(k) = 9, divided by 9.

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A001534 a(n) = (9*n+1)*(9*n+8).

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A115282 Correlation triangle for the sequence 3-2*0^n.

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A141324 Sum of digits of A002452(n).

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Maple

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A168416 a(n) = 1 + 9*floor(n/2).

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Magma

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A172174 a(n) = 90*a(n-1) + 1.

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A231233 Triangle T(n,k) = greatest prime factor of n*k+1.

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A296180 Triangle read by rows: T(n, k) = 3*(n - k)*k + 1, n >= 0, 0 <= k <= n.

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A001534 a(n) = (9n+1)(9*n+8).

A296180 Triangle read by rows: T(n, k) = 3(n - k)k + 1, n >= 0, 0 <= k <= n.