keyword:less - cp's OEIS frontend

A138121 Triangle read by rows in which row n lists the partitions of n that do not contain 1 as a part in juxtaposed reverse-lexicographical order followed by A000041(n-1) 1's.

1, 2, 1, 3, 1, 1, 4, 2, 2, 1, 1, 1, 5, 3, 2, 1, 1, 1, 1, 1, 6, 3, 3, 4, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 7, 4, 3, 5, 2, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 4, 4, 5, 3, 6, 2, 3, 3, 2, 4, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 5, 4, 6, 3, 3, 3, 3, 7, 2, 4, 3, 2, 5, 2, 2, 3, 2, 2

Offset: 1

Omar E. Pol, Mar 21 2008

Mirror of triangle A135010.

			Triangle begins:
[1];
[2],[1];
[3],[1],[1];
[4],[2,2],[1],[1],[1];
[5],[3,2],[1],[1],[1],[1],[1];
[6],[3,3],[4,2],[2,2,2],[1],[1],[1],[1],[1],[1],[1];
[7],[4,3],[5,2],[3,2,2],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1],[1];
...
The illustration of the three views of the section model of partitions (version "tree" with seven sections) shows the connection between several sequences.
---------------------------------------------------------
Partitions                A194805            Table 1.0
.  of 7       p(n)        A194551             A135010
---------------------------------------------------------
7              15                    7     7 . . . . . .
4+3                                4       4 . . . 3 . .
5+2                              5         5 . . . . 2 .
3+2+2                          3           3 . . 2 . 2 .
6+1            11    6       1             6 . . . . . 1
3+3+1                  3     1             3 . . 3 . . 1
4+2+1                    4   1             4 . . . 2 . 1
2+2+2+1                    2 1             2 . 2 . 2 . 1
5+1+1           7            1   5         5 . . . . 1 1
3+2+1+1                      1 3           3 . . 2 . 1 1
4+1+1+1         5        4   1             4 . . . 1 1 1
2+2+1+1+1                  2 1             2 . 2 . 1 1 1
3+1+1+1+1       3            1 3           3 . . 1 1 1 1
2+1+1+1+1+1     2          2 1             2 . 1 1 1 1 1
1+1+1+1+1+1+1   1            1             1 1 1 1 1 1 1
.               1                         ---------------
.               *<------- A000041 -------> 1 1 2 3 5 7 11
.                         A182712 ------->   1 0 2 1 4 3
.                         A182713 ------->     1 0 1 2 2
.                         A182714 ------->       1 0 1 1
.                                                  1 0 1
.                         A141285           A182703  1 0
.                    A182730   A182731                 1
---------------------------------------------------------
.                              A138137 --> 1 2 3 6 9 15..
---------------------------------------------------------
.       A182746 <--- 4 . 2 1 0 1 2 . 4 ---> A182747
---------------------------------------------------------
.
.       A182732 <--- 6 3 4 2 1 3 5 4 7 ---> A182733
.                    . . . . 1 . . . .
.                    . . . 2 1 . . . .
.                    . 3 . . 1 2 . . .
.      Table 2.0     . . 2 2 1 . . 3 .     Table 2.1
.                    . . . . 1 2 2 . .
.                            1 . . . .
.
.  A182982  A182742       A194803       A182983  A182743
.  A182992  A182994       A194804       A182993  A182995
---------------------------------------------------------
.
From _Omar E. Pol_, Sep 03 2013: (Start)
Illustration of initial terms (n = 1..6). The table shows the six sections of the set of partitions of 6. Note that before the dissection the set of partitions was in the ordering mentioned in A026792. More generally, the six sections of the set of partitions of 6 also can be interpreted as the first six sections of the set of partitions of any integer >= 6.
Illustration of initial terms:
---------------------------------------
n  j     Diagram          Parts
---------------------------------------
.         _
1  1     |_|              1;
.         _ _
2  1     |_  |            2,
2  2       |_|            .  1;
.         _ _ _
3  1     |_ _  |          3,
3  2         | |          .  1,
3  3         |_|          .  .  1;
.         _ _ _ _
4  1     |_ _    |        4,
4  2     |_ _|_  |        2, 2,
4  3           | |        .  1,
4  4           | |        .  .  1,
4  5           |_|        .  .  .  1;
.         _ _ _ _ _
5  1     |_ _ _    |      5,
5  2     |_ _ _|_  |      3, 2,
5  3             | |      .  1,
5  4             | |      .  .  1,
5  5             | |      .  .  1,
5  6             | |      .  .  .  1,
5  7             |_|      .  .  .  .  1;
.         _ _ _ _ _ _
6  1     |_ _ _      |    6,
6  2     |_ _ _|_    |    3, 3,
6  3     |_ _    |   |    4, 2,
6  4     |_ _|_ _|_  |    2, 2, 2,
6  5               | |    .  1,
6  6               | |    .  .  1,
6  7               | |    .  .  1,
6  8               | |    .  .  .  1,
6  9               | |    .  .  .  1,
6  10              | |    .  .  .  .  1,
6  11              |_|    .  .  .  .  .  1;
...
(End)

Robert Price, Table of n, a(n) for n = 1..16851, 25 rows
Omar E. Pol, A section model of partitions (2D and 3D) [From _Omar E. Pol_, Sep 07 2008]
Robert Price, Mathematica Program to Generate Diagram

Row n has length A138137(n).
Rows sums give A138879.
Cf. A000041, A135010, A138879, A138880, A141285, A182703, A194812, A206437, A211009.

less[run1_, run2_] := (lg1 = run1 // Length; lg2 = run2 // Length; lg = Max[lg1, lg2]; r1 = If[lg1 == lg, run1, PadRight[run1, lg, 0]]; r2 = If[lg2 == lg, run2, PadRight[run2, lg, 0]]; Order[r1, r2] != -1); row[n_] := Join[Array[1 &, {PartitionsP[n - 1]}], Sort[Reverse /@ Select[IntegerPartitions[n], FreeQ[#, 1] &], less]] // Flatten // Reverse; Table[row[n], {n, 1, 9}] // Flatten (* Jean-François Alcover, Jan 15 2013 *)
Table[Reverse/@Reverse@DeleteCases[Sort@PadRight[Reverse/@Cases[IntegerPartitions[n], x_ /; Last[x]!=1]], x_ /; x==0, 2]~Join~ConstantArray[{1}, PartitionsP[n - 1]], {n, 1, 9}]  // Flatten (* Robert Price, May 11 2020 *)

A050268 Primes of the form 36k^2 - 810k + 2753, listed in order of increasing parameter k >= 0.

Original entry on oeis.org

2753, 1979, 1277, 647, 89, 359, 953, 1619, 2357, 3167, 4049, 5003, 6029, 7127, 8297, 9539, 10853, 12239, 13697, 15227, 16829, 18503, 20249, 22067, 23957, 25919, 27953, 30059, 32237, 34487, 36809, 41669, 44207, 46817, 49499, 52253

Offset: 1

Eric W. Weisstein

The sequence of primes of this form, in order of increasing size, would read: 89, 359, 647, 953, 1277, 1619, 1979, 2357, 2753, ... - M. F. Hasler, Jan 18 2015

The polynomial is a transformed version of the polynomial P(x) = 36*x^2 + 18*x - 1801 whose absolute value gives 45 distinct primes for -33 <= x <= 11, found by Ruby in 1989. In the present sequence only positive values of the polynomial are taken into account. A117081 provides also the negative function values. - Hugo Pfoertner, Dec 13 2019

Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004.

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Jitender Singh, Prime numbers and factorization of polynomials, arXiv:2411.18366 [math.NT], 2024.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

Cf. A022464, A117081.

[a: n in [0..100] | IsPrime(a) where a is  36*n^2 - 810*n + 2753]; // Vincenzo Librandi, Dec 08 2011

t1:=[seq(36*n^2 - 810*n + 2753,n=0..100)]; t2:=[]; for i from 1 to nops(t1) do if isprime(t1[i]) then t2:=[op(t2),t1[i]]; fi; od: t2; # N. J. A. Sloane

Select[Table[36n^2-810n+2753,{n,0,2000}],PrimeQ] (* Vincenzo Librandi, Dec 08 2011 *)

select(isprime, vector(1000, n, 36*n^2-810*n+2753)) \\ Charles R Greathouse IV, Feb 14 2011

Definition corrected by M. F. Hasler, Jan 18 2015

A030341 Triangle T(n,k): write n in base 3, reverse order of digits.

Original entry on oeis.org

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

Offset: 0

Clark Kimberling

			Triangle begins :
0
1
2
0, 1
1, 1
2, 1
0, 2
1, 2
2, 2
0, 0, 1
1, 0, 1
2, 0, 1
0, 1, 1
1, 1, 1
2, 1, 1 ...

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened
Eric Weisstein's World of Mathematics, Ternary.
Wikipedia, Ternary numeral system

Cf. A081604 (row lengths), A053735 (row sums), A007089, A003137.

Cf. A030308, A030386, A031235, A030567, A031007, A031045, A031087, A031298 for the base-2 to base-10 analogs.

a030341 n k = a030341_tabf !! n !! k
a030341_row n = a030341_tabf !! n
a030341_tabf = iterate succ [0] where
   succ []     = [1]
   succ (2:ts) = 0 : succ ts
   succ (t:ts) = (t + 1) : ts
-- Reinhard Zumkeller, Feb 21 2013

A030341_row := n -> op(convert(n, base, 3)):
seq(A030341_row(n), n=0..32); # Peter Luschny, Nov 28 2017

Flatten[Table[Reverse[IntegerDigits[n,3]],{n,0,40}]] (* Harvey P. Dale, Oct 20 2014 *)

A030341(n, k=-1)=/*k<0&&error("Flattened sequence not yet implemented.")*/n\3^k%3 \\ Assuming that columns are numbered starting with k=0 as in A030308, A030567 and others. - M. F. Hasler, Jul 21 2013

Initial 0 and better name by Philippe Deléham, Oct 20 2011

A031298 Triangle T(n,k): write n in base 10, reverse order of digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 4, 0

Offset: 0

Clark Kimberling

The length of n-th row is given in A055642(n). - Reinhard Zumkeller, Jul 04 2012

According to the formula for T(n,1), columns are numbered starting with 1. One might also number columns starting with the offset 0, as to have the coefficient of 10^k in column k. - M. F. Hasler, Jul 21 2013

Reinhard Zumkeller, Rows n = 0..2500 of triangle, flattened

Cf. A030308, A030341, A030386, A031235, A030567, A031007, A031045, A031087 for the base-2 to base-9 analogs.

a031298 n k = a031298_tabf !! n !! k
a031298_row n = a031298_tabf !! n
a031298_tabf = iterate succ [0] where
   succ []     = [1]
   succ (9:ds) = 0 : succ ds
   succ (d:ds) = (d + 1) : ds
-- Reinhard Zumkeller, Jul 04 2012

Table[Reverse[IntegerDigits[n]],{n,0,50}]//Flatten (* Harvey P. Dale, Mar 07 2023 *)

T(n,k)=n\10^(k-1)%10 \\ M. F. Hasler, Jul 21 2013

T(n,1) = A010879(n); T(n,A055642(n)) = A000030(n). - Reinhard Zumkeller, Jul 04 2012

Initial 0 and better name by Philippe Deléham, Oct 20 2011

Edited by M. F. Hasler, Jul 21 2013

A048988 Primes of the form 4k^2 + 4k + 59.

Original entry on oeis.org

59, 67, 83, 107, 139, 179, 227, 283, 347, 419, 499, 587, 683, 787, 1019, 1283, 1427, 1579, 1907, 2083, 2267, 2459, 2659, 3083, 3307, 3539, 3779, 4027, 4283, 4547, 5099, 5387, 5683, 5987, 6299, 6619, 6947, 7283, 8707, 9467, 9859, 10259, 10667, 11083

Offset: 1

G. L. Honaker, Jr.

From Peter Bala, Apr 18 2018: (Start)
Let P(n) = 4*n^2 + 4*n + 59. The polynomial 1/2*P(n-1/2) = 2*n^2 + 29 has prime values for n from 0 to 28. See A007641. Also P(n-14) = 4*n^2 - 108*n + 787 is prime for the 28 consecutive values of n from 0 to 27.
The sequence of 28 values of the polynomial 4*P((n-2)/4) = n^2 + 232 for n from -1 to 26 is [233, 2^3*29, 233, 2^2*59, 241, 2^3*31, 257, 2^2*67, 281, 2^3*37, 313, 2^2*83, 353, 2^3*47, 401, 2^2*107, 457, 2^3*61, 521, 2^2*139, 593, 2^3*79, 673, 2^2*179, 761, 2^3*101, 857, 2^2*227], and consists of 7 groups of 4 numbers of the form p_1, 2^3*p_2, p_3, 2^2*p_4, where the p's are prime numbers. (End)

Seiichi Manyama, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

Cf. A005846, A007641, A271980.

[ a: n in [0..250] | IsPrime(a) where a is 4*n^2 +4*n + 59]; // Vincenzo Librandi, Nov 19 2010

select(isprime, [4*k*(k+1)+59$k=0..100])[];  # Alois P. Heinz, Apr 16 2025

Select[(4 #^2 + 4 # + 59) & /@ Range[0, 100], PrimeQ] (* Robert Price, Apr 16 2025 *)

lista(nn) = for(k=0, nn, if(isprime(p=4*k^2+4*k+59), print1(p, ", "))); \\ Altug Alkan, Apr 18 2018

A046563 First numerator and then denominator of each element of the 1/4-Pascal triangle (by row). To get a 1/4-Pascal triangle, replace "2" in the third row of the Pascal triangle with "1/4" and calculate all other rows as in the Pascal triangle.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 1, 1, 5, 4, 5, 4, 1, 1, 1, 1, 9, 4, 5, 2, 9, 4, 1, 1, 1, 1, 13, 4, 19, 4, 19, 4, 13, 4, 1, 1, 1, 1, 17, 4, 8, 1, 19, 2, 8, 1, 17, 4, 1, 1, 1, 1, 21, 4, 49, 4, 35, 2, 35, 2, 49, 4, 21, 4, 1, 1, 1, 1, 25, 4, 35, 2, 119, 4, 35, 1, 119, 4, 35, 2, 25, 4, 1, 1, 1, 1

Offset: 1

Mohammad K. Azarian

			1/1;
1/1  1/1;
1/1  1/4  1/1;
1/1  5/4  5/4  1/1;
1/1  9/4  5/2  9/4  1/1;
1/1 13/4 19/4 19/4 13/4  1/1;
1/1 17/4  8/1 19/2  8/1 17/4  1/1;
1/1 21/4 49/4 35/2 35/2 49/4 21/4 1/1; ...

A050267 Primes or negative values of primes in the sequence b(n) = 47n^2 - 1701n + 10181, n >= 0.

Original entry on oeis.org

10181, 8527, 6967, 5501, 4129, 2851, 1667, 577, -419, -1321, -2129, -2843, -3463, -3989, -4421, -4759, -5003, -5153, -5209, -5171, -5039, -4813, -4493, -4079, -3571, -2969, -2273, -1483, -599, 379, 1451, 2617, 3877, 5231, 6679, 8221, 9857, 11587, 13411, 15329, 17341, 19447, 21647, 31387

Offset: 1

Eric W. Weisstein

Terms are listed in the order of their appearance in sequence b.

This is a transformed version of the polynomial P(x) = 47*x^2 + 9*x - 5209 whose absolute value gives 43 distinct primes for -24 <= x <= 18, found by G. W. Fung in 1988. - Hugo Pfoertner, Dec 13 2019

R. K. Guy, Unsolved Problems in Number Theory, 3rd ed., Springer, 2004 (ISBN 0-387-20860-7); see Section A17, p. 59.
Paulo Ribenboim, The Little Book of Bigger Primes, Second Edition, Springer-Verlag New York, 2004. See p. 147.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
G. W. Fung and H. C. Williams, Quadratic polynomials which have a high density of prime values, Math. Comput. 55(191) (1990), 345-353.
Carlos Rivera, Problem 12: Prime producing polynomials, The Prime Puzzles & Problems Connection.
Jitender Singh, Prime numbers and factorization of polynomials, arXiv:2411.18366 [math.NT], 2024.
Eric Weisstein's World of Mathematics, Prime-Generating Polynomial.

Cf. A002383, A005471, A005846, A007635, A022464, A027753, A027755, A027758, A048059, A050267, A050268, A116206, A117081, A267252.

lst={};Do[p=47*n^2-1701*n+10181;If[PrimeQ[p],AppendTo[lst,p]],{n,0,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jan 29 2009 *)
Select[Table[47n^2-1701n+10181,{n,0,50}],PrimeQ] (* Harvey P. Dale, Oct 03 2011 *)

[n | n <- apply(m->47*m^2-1701*m+10181, [0..100]), isprime(abs(n))] \\ Charles R Greathouse IV, Jun 18 2017

Edited by N. J. A. Sloane, May 10 2007
Further edited by Klaus Brockhaus, Mar 20 2010
More terms (to distinguish from quadratic) from Charles R Greathouse IV, Jun 18 2017

A176246 a(n) = A001223(n+1) - 1.

Original entry on oeis.org

1, 1, 3, 1, 3, 1, 3, 5, 1, 5, 3, 1, 3, 5, 5, 1, 5, 3, 1, 5, 3, 5, 7, 3, 1, 3, 1, 3, 13, 3, 5, 1, 9, 1, 5, 5, 3, 5, 5, 1, 9, 1, 3, 1, 11, 11, 3, 1, 3, 5, 1, 9, 5, 5, 5, 1, 5, 3, 1, 9, 13, 3, 1, 3, 13, 5, 9, 1, 3, 5, 7, 5, 5, 3, 5, 7, 3, 7, 9, 1, 9, 1, 5, 3, 5, 7, 3, 1, 3, 11, 7, 3, 7

Offset: 1

Edmund Algeo, Apr 13 2010

Previous name was: Numbers which added to an odd prime plus one, yield the next prime in the series for primes.

Essentially a duplicate of A046933 and A135732. - T. D. Noe, Oct 23 2013

Cf. A046933 (number of composites between successive primes).

Differences[Prime[Range[2, 100]]] - 1 (* Paolo Xausa, Jul 02 2025 *)

a(n) = A001223(n+1) - 1. - Michel Marcus, Jun 08 2013

New name using formula from Michel Marcus, Joerg Arndt, Oct 22 2013

A271980 Numbers k such that 3k^2 + 39k + 37 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 25, 26, 29, 30, 31, 32, 33, 34, 35, 38, 39, 40, 41, 42, 44, 45, 46, 48, 49, 51, 52, 53, 54, 55, 57, 58, 59, 60, 63, 64, 66, 68, 69, 70, 71, 72, 79, 84, 86, 88, 89, 90, 91, 92

Offset: 1

Robert Price, Apr 17 2016

From Peter Bala, Apr 16 2018: (Start)
Let P(n) = 3*n^2 + 39*n + 37. The absolute values of the polynomial P(2*n - 29) = 12*n^2 - 270*n + 1429 for n from 0 to 27 are distinct primes, except at n = 14 when the value is 1.
The absolute values of the polynomial 3*P((n - 20)/3) = n^2 - n - 269 for n from 0 to 42 are either prime or 3 times a prime.
The absolute values of the polynomial 3*P((4*n - 89)/3) = 16*n^2 - 556*n + 4561 for n from 0 to 27 are either prime or 3 times a prime. (End)

			4 is in this sequence since 3*4^2 + 39*4 + 37 = 48+156+37 = 241 is prime.

Robert Price, Table of n, a(n) for n = 1..3510
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A256585, A050265 - A050268, A005846, A007641, A007635, A048988.

[n: n in [0..100] |IsPrime(3*n^2+39*n+37)]; // Vincenzo Librandi, Apr 19 2018

Select[Range[0, 100], PrimeQ[3*#^2 + 39*# + 37] &]

isok(n) = isprime(3*n^2 + 39*n + 37); \\ Michel Marcus, Apr 17 2016

lista(nn) = for(n=0, nn, if(ispseudoprime(3*n^2+39*n+37), print1(n, ", "))); \\ Altug Alkan, Apr 18 2016

A272074 Numbers k such that k^4 + 29*k^2 + 101 is prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 23, 26, 31, 32, 34, 35, 37, 43, 44, 45, 47, 49, 53, 56, 60, 61, 62, 66, 67, 68, 70, 71, 72, 74, 75, 79, 80, 81, 84, 85, 89, 90, 91, 93, 96, 99

Offset: 1

Robert Price, Apr 19 2016

			4 is in this sequence since 4^4 + 29*4^2 + 101 = 256+464+101 = 821 is prime.

Robert Price, Table of n, a(n) for n = 1..2264
Eric Weisstein's World of Mathematics, Prime-Generating Polynomials

Cf. A050265 - A050268, A005846, A007641, A007635, A048988, A256585.

Cf. A271980, A272075.

Select[Range[0,100],PrimeQ[#^4+29#^2+101]&] (* Harvey P. Dale, Dec 15 2020 *)

lista(nn) = for(n=0, nn, if(ispseudoprime(n^4+29*n^2+101), print1(n, ", "))); \\ Altug Alkan, Apr 19 2016

cp's OEIS Frontend

A138121 Triangle read by rows in which row n lists the partitions of n that do not contain 1 as a part in juxtaposed reverse-lexicographical order followed by A000041(n-1) 1's.

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A050268 Primes of the form 36*k^2 - 810*k + 2753, listed in order of increasing parameter k >= 0.

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A030341 Triangle T(n,k): write n in base 3, reverse order of digits.

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A031298 Triangle T(n,k): write n in base 10, reverse order of digits.

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A048988 Primes of the form 4*k^2 + 4*k + 59.

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Magma

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A046563 First numerator and then denominator of each element of the 1/4-Pascal triangle (by row). To get a 1/4-Pascal triangle, replace "2" in the third row of the Pascal triangle with "1/4" and calculate all other rows as in the Pascal triangle.

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Examples

A050267 Primes or negative values of primes in the sequence b(n) = 47*n^2 - 1701*n + 10181, n >= 0.

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A050268 Primes of the form 36k^2 - 810k + 2753, listed in order of increasing parameter k >= 0.

A048988 Primes of the form 4k^2 + 4k + 59.

A050267 Primes or negative values of primes in the sequence b(n) = 47n^2 - 1701n + 10181, n >= 0.

A271980 Numbers k such that 3k^2 + 39k + 37 is prime.