A059100 -id:A059100 - cp's OEIS frontend

A253639 Lesser of twin primes of the form (k^2 + 2, k^2 + 4).

3, 11, 227, 1091, 2027, 3251, 13691, 21611, 59051, 65027, 91811, 140627, 178931, 199811, 205211, 227531, 328331, 567011, 700571, 804611, 815411, 1071227, 2241011, 3629027, 4223027, 4347227, 4809251, 5212091, 5919491, 6185171, 6426227, 6671891, 7601051, 7969331, 8661251, 8732027, 9018011, 10323371

Offset: 1

M. F. Hasler, Jan 16 2015

Companion sequence to A085554 (which yields the greater of the pair) and A086381 (which lists the x-values). Except for the first term, all values are a(n)=11 (mod 72). - M. F. Hasler, Jan 18 2015

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

Cf. A001097, A001359, A006512, A085554, A086381, A253640.

Transpose[Select[Table[x^2+{2,4},{x,5000}],AllTrue[#,PrimeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *)

forstep(x=1,9999,2,is_A086381(x)&&print1(x^2+2,",")) \\ M. F. Hasler, Jan 16 2015

Equals A059100 o A086381 = A023444 o A085554, i.e., a(n) = A086381(n)^2+2 = A085554(n)-2. - M. F. Hasler, Jan 18 2015

A270109 a(n) = n^3 + (n+1)*(n+2).

Original entry on oeis.org

2, 7, 20, 47, 94, 167, 272, 415, 602, 839, 1132, 1487, 1910, 2407, 2984, 3647, 4402, 5255, 6212, 7279, 8462, 9767, 11200, 12767, 14474, 16327, 18332, 20495, 22822, 25319, 27992, 30847, 33890, 37127, 40564, 44207, 48062, 52135, 56432, 60959, 65722, 70727, 75980, 81487, 87254

Offset: 0

Bruno Berselli, Mar 11 2016, at the suggestion of Giuseppe Amoruso in BASE Cinque forum

For n>1, many consecutive terms of the sequence are generated by floor(sqrt(n^2 + 2)^3) + n^2 + 2.
It appears that this is a subsequence of A000037 (the nonsquares).
The primes in the sequence belong to A045326.
Inverse binomial transform is 2, 5, 8, 6, 0, 0, 0, ... (0 continued).

Bruno Berselli, Table of n, a(n) for n = 0..1000
MathsSmart, Number pattern and Puzzle - 7, 20, 47, 94, 167.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Subsequence of A001651, A047212.
Cf. A000037, A045326.
Cf. A027444: numbers of the form n^3+n*(n+1); A085490: numbers of the form n^3+(n-1)*n.
Cf. A008865: numbers of the form n+(n+1)*(n+2); A130883: numbers of the form n^2+(n+1)*(n+2).

Magma
```
[n^3+(n+1)*(n+2): n in [0..50]];
```

Table[n^3 + (n + 1) (n + 2), {n, 0, 50}]

Maxima
```
makelist(n^3+(n+1)*(n+2), n, 0, 50);
```
PARI
```
vector(50, n, n--; n^3+(n+1)*(n+2))
```
Sage
```
[n^3+(n+1)*(n+2) for n in (0..50)]
```

O.g.f.: (2 - x + 4*x^2 + x^3)/(1 - x)^4.
E.g.f.: (2 + x)*(1 + x)^2*exp(x).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4), n>3.
a(n+h) - a(n) + a(n-h) = n^3 + n^2 + (6*h^2+3)*n + (2*h^2+2) for any h. This identity becomes a(n) = n^3 + n^2 + 3*n + 2 if h=0.
a(h*a(n) + n) = (h*a(n))^3 + (3*n+1)*(h*a(n))^2 + (3*n^2+2*n+3)*(h*a(n)) + a(n) for any h, therefore a(h*a(n) + n) is always a multiple of a(n).
a(n) + a(-n) = 2*A059100(n) = A255843(n).
a(n) - a(-n) = 4*A229183(n).

A156798 a(n) = n^4 + 5*n^2 + 4.

Original entry on oeis.org

4, 10, 40, 130, 340, 754, 1480, 2650, 4420, 6970, 10504, 15250, 21460, 29410, 39400, 51754, 66820, 84970, 106600, 132130, 162004, 196690, 236680, 282490, 334660, 393754, 460360, 535090, 618580, 711490, 814504, 928330, 1053700, 1191370

Offset: 0

Reinhard Zumkeller, Feb 16 2009

Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Cf. A000290, A002522, A059100, A087475.

Magma
```
[n^4+5*n^2+4: n in [0..50]];
```
Mathematica
```
Table[n^4+5n^2+4, {n,0,40}]
```
PARI
```
a(n)=n^4+5*n^2+4
```

[(n^2 +1)*(n^2 +4) for n in (0..50)] # G. C. Greubel, Jun 10 2021

a(n) = A002522(n)*A087475(n) = A000290(n) + A000290(A059100(n)) = A028552(A002522(n)).
a(n) = (n^2 + 1)*(n^2 + 4) = n^2 + (n^2 + 2)^2.
G.f.: 2*(2 -5*x +15*x^2 -5*x^3 +5*x^4)/(1-x)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009; corrected by R. J. Mathar, Sep 16 2009
a(0)=4, a(1)=10, a(2)=40, a(3)=130, a(4)=340, a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5). - Harvey P. Dale, May 04 2011
From Amiram Eldar, Jan 18 2021: (Start)
Sum_{n>=0} 1/a(n) = (1 + Pi*coth(Pi))/8 - Pi*tanh(Pi)/24.
Sum_{n>=0} (-1)^n/a(n) = 1/8 + Pi*csch(Pi)/6 - Pi*csch(Pi)*sech(Pi)/24. (End)
E.g.f.: (4 + 6*x + 12*x^2 + 6*x^3 + x^4)*exp(x). - G. C. Greubel, Jun 10 2021

A160842 Number of lines through at least 2 points of a 2 X n grid of points.

Original entry on oeis.org

0, 1, 6, 11, 18, 27, 38, 51, 66, 83, 102, 123, 146, 171, 198, 227, 258, 291, 326, 363, 402, 443, 486, 531, 578, 627, 678, 731, 786, 843, 902, 963, 1026, 1091, 1158, 1227, 1298, 1371, 1446, 1523, 1602, 1683, 1766, 1851, 1938, 2027, 2118, 2211, 2306, 2403, 2502

Offset: 0

Seppo Mustonen, May 28 2009

Vincenzo Librandi, Table of n, a(n) for n = 0..10000
S. Mustonen, On lines and their intersection points in a rectangular grid of points
Seppo Mustonen, On lines and their intersection points in a rectangular grid of points [Local copy]
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A295707, A107348.

[0,1] cat [n^2 + 2: n in [2..100]]; // G. C. Greubel, Apr 30 2018

a[n_]:=If[n<2,n,n^2+2] Table[a[n],{n,0,50}]
Join[{0,1},Range[2,50]^2+2] (* Harvey P. Dale, Feb 06 2015 *)

Vec(-x*(2*x^3-4*x^2+3*x+1) / (x-1)^3 + O(x^100)) \\ Colin Barker, May 24 2015

a(n) = n^2 + 2 = A059100(n) = A010000(n) for n > 1.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 4. - Colin Barker, May 24 2015
G.f.: -x*(2*x^3 - 4*x^2 + 3*x + 1) / (x-1)^3. - Colin Barker, May 24 2015
Sum_{n>=1} 1/a(n) = Pi * coth(sqrt(2)*Pi) / 2^(3/2) - 1/4. - Vaclav Kotesovec, May 01 2018

A163253 An interspersion: the order array of the odd-numbered columns of the double interspersion at A161179.

Original entry on oeis.org

1, 4, 2, 9, 5, 3, 16, 10, 7, 6, 25, 17, 13, 11, 8, 36, 26, 21, 18, 14, 12, 49, 37, 31, 27, 22, 19, 15, 64, 50, 43, 38, 32, 28, 23, 20, 81, 65, 57, 51, 44, 39, 33, 29, 24, 100, 82, 73, 66, 58, 52, 45, 40, 34, 30, 121, 101, 91, 83, 74, 67, 59, 53, 46, 41, 35

Offset: 1

Clark Kimberling, Jul 23 2009

A permutation of the natural numbers.
Row 1 consists of the squares.
Beginning with row 5, the columns obey a 3rd-order recurrence:
c(n)=c(n-1)+c(n-2)-c(n-3)+1; thus disregarding row 1, the nonsquares are partitioned by this recurrence.
Except for initial terms, the first ten rows match A000290, A002522, A002061, A059100, A014209, A117950, A027688, A087475, A027689, A117951, and the first column, A035106.

			Corner:
1....4....9...16...25
2....5...10...17...26
3....7...13...21...31
6...11...18...27...38
The double interspersion A161179 begins thus:
1....4....7...12...17...24
2....3....8...11...18...23
5....6...13...16...25...30
9...10...19...22...33...38
Expel the even-numbered columns, leaving
1....7...17...
2....8...18...
5...13...25...
9...19...33...
Then replace each of those numbers by its rank when all the numbers are jointly ranked.

Clark Kimberling, Doubly interspersed sequences, double interspersions and fractal sequences, The Fibonacci Quarterly 48 (2010) 13-20.

Cf. A000037, A000290, A161179, A163254, A163255, A163256, A163257, A163258.

Let S(n,k) denote the k-th term in the n-th row. Three cases:
S(1,k)=k^2;
if n is even, then S(n,k)=k^2+(n-2)k+(n^2-2*n+4)/4;
if n>=3 is odd, then S(n,k)=k^2+(n-2)k+(n^2-2*n+1)/4.

Edited and augmented by Clark Kimberling, Jul 24 2009

A189836 a(n) = n^2 + 11.

Original entry on oeis.org

11, 12, 15, 20, 27, 36, 47, 60, 75, 92, 111, 132, 155, 180, 207, 236, 267, 300, 335, 372, 411, 452, 495, 540, 587, 636, 687, 740, 795, 852, 911, 972, 1035, 1100, 1167, 1236, 1307, 1380, 1455, 1532, 1611, 1692, 1775, 1860, 1947

Offset: 0

Vladimir Joseph Stephan Orlovsky, Apr 28 2011

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Cf. A002522, A059100, A117950, A087475.

[n^2 + 11: n in [0..50]]; // G. C. Greubel, Jan 13 2018

Table[n^2+11,{n,0,100}]
LinearRecurrence[{3,-3,1},{11,12,15},60] (* Harvey P. Dale, Aug 24 2020 *)

a(n)=n^2+11 \\ Charles R Greathouse IV, Jun 17 2017

From G. C. Greubel, Jan 13 2018: (Start)
G.f.: (11 - 21*x + 12*x^2)/(1 - x)^3.
E.g.f.: (11 + x + x^2)*exp(x). (End)
From Amiram Eldar, Nov 02 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(11)*Pi*coth(sqrt(11)*Pi))/22.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(11)*Pi*cosech(sqrt(11)*Pi))/22. (End)
From Amiram Eldar, Feb 12 2024: (Start)
Product_{n>=0} (1 - 1/a(n)) = sqrt(10/11)*sinh(sqrt(10)*Pi)/sinh(sqrt(11)*Pi).
Product_{n>=0} (1 + 1/a(n)) = 2*sqrt(3/11)*sinh(2*sqrt(3)*Pi)/sinh(sqrt(11)*Pi). (End)

A132282 Near-cube primes: primes of the form p^3 + 2, where p is noncomposite.

Original entry on oeis.org

2, 3, 29, 127, 24391, 357913, 571789, 1442899, 5177719, 18191449, 30080233, 73560061, 80062993, 118370773, 127263529, 131872231, 318611989, 344472103, 440711083, 461889919, 590589721, 756058033, 865523179, 1095912793

Offset: 1

Jonathan Vos Post, Aug 16 2007

The corresponding near-cube prime indices q are A132281. Analog of near-square primes. After a(1) = 2, all values must be odd. Numbers of the form n^2+2 for n=1, 2, ... are 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, ... (A059100). These are prime for indices n = 1, 3, 9, 15, 21, 33, 39, 45, 57, 81, 99, ... (A067201), corresponding to the near-square primes 3, 11, 83, 227, 443, 1091, 1523, 2027, ... (A056899). Helfgott proves with minor conditions that: "Let f be a cubic polynomial. Then there are infinitely many primes p such that f(p) is squarefree." Note that 47^3 + 2 = 103825 = 5^2 * 4153 and similarly 97^3 + 2 is divisible by 5^2, but otherwise an infinite number of p^3+2 are squarefree.

			a(1) = 0^3 + 2 = 2 is prime and 0 is noncomposite.
a(2) = 1^3 + 2 = 3 is prime and 1 is noncomposite.
a(3) = 3^3 + 2 = 29 is prime and 3 is prime.
a(4) = 5^3 + 2 = 127 is prime and 5 is prime.
a(5) = 29^3 + 2 = 24391 is prime and 29 is prime.
45^3 + 2 = 91127 is prime, but not in this sequence because 45 is not prime.
63^3 + 2 = 250049 is prime, but not in this sequence because 63 is not prime.
a(6) = 71^3 + 2 = 357913 is prime.
a(7) = 83^3 + 2 = 571789 is prime.
a(8) = 113^3 + 2 = 1442899 is prime.

Harald Andres Helfgott, Power-free values, repulsion between points, differing beliefs and the existence of error, arXiv:0706.1497 [math.NT], 2007.

Cf. A000040, A048636, A056899, A059100, A067200, A067201, A084380, A132281.

Join[{2, 5}, Select[Prime[Range[200]]^3 + 2, PrimeQ[ # ] &]] (* Stefan Steinerberger, Aug 17 2007 *)

v=[2,3]; forprime(p=3, 1e4, if(isprime(t=p^3+2), v=concat(v, t))); t \\ Charles R Greathouse IV, Feb 14 2011

a(n) = A132281(n)^3 + 2. {p in A000040 such that for some q = 0, 1, or q in A000040, we have p = A067200(q) = A084380(q) = q^3 + 2 is in A000040}.

a(n) = A048636(n-2) for n >= 3. - Georg Fischer, Nov 03 2018

More terms from Stefan Steinerberger, Aug 17 2007

a(2) corrected by Charles R Greathouse IV, Feb 14 2011

A230584 Either two less than a square or two more than a square.

Original entry on oeis.org

2, 3, 6, 7, 11, 14, 18, 23, 27, 34, 38, 47, 51, 62, 66, 79, 83, 98, 102, 119, 123, 142, 146, 167, 171, 194, 198, 223, 227, 254, 258, 287, 291, 322, 326, 359, 363, 398, 402, 439, 443, 482, 486, 527, 531, 574, 578, 623, 627, 674, 678, 727, 731, 782, 786, 839, 843, 898, 902, 959, 963

Offset: 1

Ralf Stephan, Oct 24 2013

Numbers n such that the polynomial x^4 - n*x^2 + 1 is reducible.
The corresponding factorizations are (x^2 + k*x - 1)*(x^2 - k*x - 1) == x^4 - (k^2 + 2)*x^2 + 1 and (x^2 + k*x + 1)*(x^2 - k*x + 1) == x^4 - (k^2 - 2)*x^2 + 1. - Joerg Arndt, Feb 07 2015
Union of A008865 and A059100.
For k > 1: a(2*k+1) - a(2*k) = 4 and a(2*k) - a(2*k-1) = k - 1; for n > 4: a(n) - a(n-2) = 2*floor(n/2) + 1 = A109613(n). - Reinhard Zumkeller, Feb 10 2015

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Cf. A008865, A059100, A000290, A109613.

import Data.List (transpose)
a230584 n = a230584_list !! (n-1)
a230584_list = 2 : 3 : concat
               (transpose [drop 2 a059100_list, drop 2 a008865_list])
-- Reinhard Zumkeller, Feb 10 2015

PARI
```
is(n)=issquare(n-2)||issquare(n+2)
```

A230584_vec(N)=Vec((2+x-x^2-x^3+2*x^5-x^6)/((1-x)^3*(1+x)^2)+O(x^N)) \\ M. F. Hasler, Oct 26 2013

From Colin Barker, Oct 24 2013: (Start)
  a(n) = (5-13*(-1)^n+2*(3+(-1)^n)*n+2*n^2)/8 for n>2.
  a(n) = (n^2+4*n-4)/4 for n>2 and even.
  a(n) = (n^2+2*n+9)/4 for n>2 and odd.
  a(n) = a(n-1)+2*a(n-2)-2*a(n-3)-a(n-4)+a(n-5) for n>7.
  G.f.: x*(x^6-2*x^5+x^3+x^2-x-2) / ((x-1)^3*(x+1)^2). (End)
After the first two terms 0^2+2 = 2^2-2, 1^2+2, the squares are sufficiently spaced to ensure that the sequence continues 2^2+2, 3^2-2, 3^2+2, 4^2-2, 4^2+2,..., i.e., a(2n-1) = n^2+2, a(2n)=(n+1)^2-2. - M. F. Hasler, Oct 26 2013

A352362 Array read by ascending antidiagonals. T(n, k) = L(k, n) where L are the Lucas polynomials.

Original entry on oeis.org

2, 2, 0, 2, 1, 2, 2, 2, 3, 0, 2, 3, 6, 4, 2, 2, 4, 11, 14, 7, 0, 2, 5, 18, 36, 34, 11, 2, 2, 6, 27, 76, 119, 82, 18, 0, 2, 7, 38, 140, 322, 393, 198, 29, 2, 2, 8, 51, 234, 727, 1364, 1298, 478, 47, 0, 2, 9, 66, 364, 1442, 3775, 5778, 4287, 1154, 76, 2

Offset: 0

Peter Luschny, Mar 18 2022

			Array starts:
n\k 0, 1,  2,   3,    4,     5,      6,       7,        8, ...
--------------------------------------------------------------
[0] 2, 0,  2,   0,    2,     0,      2,       0,        2, ... A010673
[1] 2, 1,  3,   4,    7,    11,     18,      29,       47, ... A000032
[2] 2, 2,  6,  14,   34,    82,    198,     478,     1154, ... A002203
[3] 2, 3, 11,  36,  119,   393,   1298,    4287,    14159, ... A006497
[4] 2, 4, 18,  76,  322,  1364,   5778,   24476,   103682, ... A014448
[5] 2, 5, 27, 140,  727,  3775,  19602,  101785,   528527, ... A087130
[6] 2, 6, 38, 234, 1442,  8886,  54758,  337434,  2079362, ... A085447
[7] 2, 7, 51, 364, 2599, 18557, 132498,  946043,  6754799, ... A086902
[8] 2, 8, 66, 536, 4354, 35368, 287298, 2333752, 18957314, ... A086594
[9] 2, 9, 83, 756, 6887, 62739, 571538, 5206581, 47430767, ... A087798
A007395|A059100|
    A001477 A079908

Eric Weisstein's World of Mathematics, Lucas Polynomial

Rows: A010673, A000032, A002203, A006497, A014448, A087130, A085447, A086902, A086594, A087798.
Columns: A007395, A001477, A059100, A079908.
Cf. A320570 (main diagonal), A114525, A309220 (variant), A117938 (variant), A352361 (Fibonacci polynomials), A350470 (Jacobsthal polynomials).

T := (n, k) -> (n/2 + sqrt((n/2)^2 + 1))^k + (n/2 - sqrt((n/2)^2 + 1))^k:
seq(seq(simplify(T(n - k, k)), k = 0..n), n = 0..10);

Table[LucasL[k, n], {n, 0, 9}, {k, 0, 9}] // TableForm
(* or *)
T[ 0, k_] := 2 Mod[k+1, 2]; T[n_, 0] := 2;
T[n_, k_] := n^k Hypergeometric2F1[1/2 - k/2, -k/2, 1 - k, -4/n^2];
Table[T[n, k], {n, 0, 9}, {k, 0, 8}] // TableForm

T(n, k) = ([0, 1; 1, k]^n*[2; k])[1, 1] ;
export(T)
for(k = 0, 9, print(parvector(10, n, T(n - 1, k))))

T(n, k) = Sum_{j=0..floor(k/2)} binomial(k-j, j)*(k/(k-j))*n^(k-2*j) for k >= 1.
T(n, k) = (n/2 + sqrt((n/2)^2 + 1))^k + (n/2 - sqrt((n/2)^2 + 1))^k.
T(n, k) = [x^k] ((2 - n*x)/(1 - n*x - x^2)).
T(n, k) = n^k*hypergeom([1/2 - k/2, -k/2], [1 - k], -4/n^2) for n,k >= 1.

A132281 Noncomposites in A067200. Noncomposites (0, 1) and primes p such that A084380(p) = p^3 + 2 is prime.

Original entry on oeis.org

0, 1, 3, 5, 29, 71, 83, 113, 173, 263, 311, 419, 431, 491, 503, 509, 683, 701, 761, 773, 839, 911, 953, 1031, 1091, 1103, 1151, 1193, 1259, 1283, 1373, 1451, 1523, 1583, 1601, 1733, 1823, 1889, 1931, 2099, 2153, 2213, 2273, 2339, 2351, 2441, 2531, 2543

Offset: 1

Jonathan Vos Post, Aug 16 2007

The corresponding near-cube primes are A132282. Analog of near-square primes. After a(1) = 0, all values must be odd. Numbers of the form n^2+2 for n=1, 2, ... are 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, ... (A059100). These are prime for indices n = 1, 3, 9, 15, 21, 33, 39, 45, 57, 81, 99, ... (A067201), corresponding to the near-square primes 3, 11, 83, 227, 443, 1091, 1523, 2027, ... (A056899). Helfgott proves with minor conditions that: "Let f be a cubic polynomial. Then there are infinitely many primes p such that f(p) is squarefree." Note that 47^3 + 2 = 103825 = 5^2 * 4153 and similarly 97^3 + 2 is divisible by 5^2, but otherwise an infinite number of p^3+2 are squarefree.

			a(1) = 0 because 0^3 + 2 = 2 is prime and 0 is noncomposite.
a(2) = 1 because 1^3 + 2 = 5 is prime and 1 is noncomposite.
a(3) = 3 because 3^3 + 2 = 29 is prime and 3 is prime.
a(4) = 5 because 5^3 + 2 = 127 is prime and 5 is prime.
a(5) = 29 because 29^3 + 2 = 24391 is prime.
45 is not in the sequence because, although 45^3 + 2 = 91127 is prime, 45 is not prime.
63 is not in the sequence because, although 63^3 + 2 = 250049 is prime, 63 is not prime.
65 is not in the sequence because, although 65^3 + 2 = 274627 is prime, 65 is not prime.
a(6) = 71 because 71^3 + 2 = 357913 is prime.
a(7) = 83 because 83^3 + 2 = 571789 is prime.
a(8) = 113 because 113^3 + 2 = 1442899 is prime.
123 is not in the sequence because, although 123^3 + 2 = 1860869 is prime, 123 is not prime.

Amiram Eldar, Table of n, a(n) for n = 1..10000
Harald Andres Helfgott, Power-free values, repulsion between points, differing beliefs and the existence of error, arXiv:0706.1497 [math.NT], 2007.

Cf. A000040, A056899, A059100, A067200, A067201, A084380, A132282.

{p in A000040 such that A067200(p) = A084380(p) = p^3 + 2 is in A000040}.

Union of {0,1} and A048637. - R. J. Mathar, Oct 18 2007

More terms from R. J. Mathar, Oct 18 2007

cp's OEIS Frontend

A253639 Lesser of twin primes of the form (k^2 + 2, k^2 + 4).

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A270109 a(n) = n^3 + (n+1)*(n+2).

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A156798 a(n) = n^4 + 5*n^2 + 4.

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Sage

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A160842 Number of lines through at least 2 points of a 2 X n grid of points.

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Magma

Mathematica

PARI

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A163253 An interspersion: the order array of the odd-numbered columns of the double interspersion at A161179.

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Formula

Extensions

A189836 a(n) = n^2 + 11.

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Magma

Mathematica

PARI

Formula

A132282 Near-cube primes: primes of the form p^3 + 2, where p is noncomposite.

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Mathematica