, 0|1] = t[n - cp's OEIS frontend

User: , 0|1] = t[n

, 0|1] = t[n has authored 6335 sequences. Here are the ten most recent ones:

A386822 Irregular table T(n,k) = Product_{j = 1..k} prime(j)^(n-j+1), n >= 0, k = 1..n.

1, 2, 4, 12, 8, 72, 360, 16, 432, 10800, 75600, 32, 2592, 324000, 15876000, 174636000, 64, 15552, 9720000, 3333960000, 403409160000, 5244319080000, 128, 93312, 291600000, 700131600000, 931875159600000, 157486901972400000, 2677277333530800000

Offset: 0

Michael De Vlieger, Aug 31 2025

Proper subset of A025487, in turn a proper subset of A055932.
For n > 1, T(n,n) is in A332785.
For 1 < k < n, T(n,k) is in A286708, where A286708 is the sequence of powerful numbers (i.e., in A001694) that are not prime powers.
For n > 1 and k > 1, T(n,k) is in A126706.

			Table begins:
  n\k   1      2        3          4           5
  ----------------------------------------------
  0:    1;
  1:    2;
  2:    4,    12;
  3:    8,    72,     360;
  4:   16,   432,   10800,     75600;
  5:   32,  2592,  324000,  15876000,  174636000;
Table of n, a(n) = P(k)^m * Q(k), for n < 12, illustrating prime power factor exponents, where k = omega(a(n)) = A001221(a(n)), P = A002110, and Q = A006939:
                                     Exponents of
 n     a(n)                  k   m   2.3.5.7
---------------------------------------------------
 1       1                           .
 2       2 = P(1)^0 * Q(1)   1   0   1
 3       4 = P(1)^1 * Q(1)   1   1   2
 4      12 = P(2)^0 * Q(2)   2   0   2.1
 5       8 = P(1)^2 * Q(1)   1   2   3
 6      72 = P(2)^1 * Q(2)   2   1   3.2
 7     360 = P(3)^0 * Q(3)   3   0   3.2.1
 8      16 = P(1)^3 * Q(1)   1   3   4
 9     432 = P(2)^2 * Q(2)   2   2   4.3
10   10800 = P(3)^1 * Q(3)   3   1   4.3.2
11   75600 = P(4)^0 * Q(4)   4   0   4.3.2.1

Michael De Vlieger, Table of n, a(n) for n = 0..703 (rows n = 0..37, flattened.)

Cf. A000079, A001694, A006939, A025487, A055932, A126706, A286708, A332785, A387491.

Table[Product[Prime[j]^(n - j + 1), {j, k}], {n, 8}, {k, n}] // Flatten

T(0,1) = 1 by convention.
T(n,1) = A000079(n) = 2^n.
T(n,n) = A006939(n).

A385674 Triangle read by rows: T(n,n) = 1 and T(n,k) = (T(n-1,k) | T(n-2,k) | ... | T(n-k,k)) + 1, where | is bitwise OR, (0<=k<=n).

Original entry on oeis.org

1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 4, 4, 2, 1, 1, 5, 7, 4, 2, 1, 1, 6, 8, 8, 4, 2, 1, 1, 7, 16, 15, 8, 4, 2, 1, 1, 8, 25, 16, 16, 8, 4, 2, 1, 1, 9, 26, 32, 31, 16, 8, 4, 2, 1, 1, 10, 28, 64, 32, 32, 16, 8, 4, 2, 1, 1, 11, 31, 113, 64, 63, 32, 16, 8, 4, 2, 1, 1, 12, 32, 114, 128, 64, 64, 32, 16, 8, 4, 2, 1

Offset: 0

Natalia L. Skirrow, Aug 04 2025

For the purposes of the recurrence, the region of the array above the triangle is filled with 0's.

In the cellular automaton, on binary representations, that starts with s = 2^n-1 on iteration t=0, then each iteration sets s := s XOR (s<<1 AND s<<2 AND ... AND s<

With respect to n, T(n,k) is in Theta(n^k); this corresponds with the k-th cellular automaton growing with width Theta(t^(1/k)).

Rows are not always unimodal! Row 18 (1 < 18 < 104 < 512 > 496 < 1986 < 2048 > 1024 > 512 = 512 > 256 > 128 > 64 > 32 > 16 > 8 > 4 > 2 > 1) is the first exception.

			Table begins
  n\k| 0  1  2   3   4   5   6   7   8  9 10 11 12 13 14 15
  ---+-----------------------------------------------------
   0 | 1
   1 | 1  1
   2 | 1  2  1
   3 | 1  3  2   1
   4 | 1  4  4   2   1
   5 | 1  5  7   4   2   1
   6 | 1  6  8   8   4   2   1
   7 | 1  7 16  15   8   4   2   1
   8 | 1  8 25  16  16   8   4   2   1
   9 | 1  9 26  32  31  16   8   4   2  1
  10 | 1 10 28  64  32  32  16   8   4  2  1
  11 | 1 11 31 113  64  63  32  16   8  4  2  1
  12 | 1 12 32 114 128  64  64  32  16  8  4  2  1
  13 | 1 13 64 116 256 128 127  64  32 16  8  4  2  1
  14 | 1 14 97 120 481 256 128 128  64 32 16  8  4  2  1
  15 | 1 15 98 127 482 512 256 255 128 64 32 16  8  4  2  1
Binary expansions of the k=2 column:
  . . . . . . . . . . . . 11111111111111111111111
  . . . . . . . . . . . .1 1111111111111111111111
  . . . . . . 11111111111 . . . . . . 11111111111
  . . . . . .1 1111111111 . . . . . .1 1111111111
  . . . 11111 . . . 11111 . . . 11111 . . . 11111
  . . .1 1111 . . .1 1111 . . .1 1111 . . .1 1111
  . .11 . .11 . .11 . .11 . .11 . .11 . .11 . .11
  . 1 1 . 1 1 . 1 1 . 1 1 . 1 1 . 1 1 . 1 1 . 1 1
  .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1 .1
The recurrence emulates binary counting, albeit with k X k 'metabits' in this diagram; the bit being  carried to is filled along the diagonal, followed by a single number in which all metabits are full and the 0th bit is on.

Paolo Xausa, Table of n, a(n) for n = 0..11475 (rows 0..150 of triangle, flattened).
Natalia L. Skirrow, on nearsighted binary counters, theorems 1 and 2 (in which T(k,n) is written as the function o(k) for the n-th cellular automaton).

Cf. A338888 (column k=2).

A351995[n_, k_] := If[n <= 1, n, Total[2^(k*(Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]] - 1))]];
A385674[n_, k_] := 2*(2^k - 1)*A351995[#[[1]], k] + If[#[[2]] == k, 1, 2*2^(k*IntegerExponent[#[[1]], 2])*(1 + 2^#[[2]] - 2^k)] & [QuotientRemainder[n, k + 1]];
Table[A385674[n, k], {n, 0, 15}, {k, 0, n}] (* Paolo Xausa, Sep 04 2025 *)

lista(nn) = my(m=matrix(nn, nn)); for (n=1, nn, m[n,n] = 1; for (k=1, n-1, for (i=1, k-1, m[n,k] = bitor(m[n,k], m[n-i,k]);); m[n,k]++;);); my(vrows=vector(nn, i, vector(i, k, m[i,k]))); vrows; \\ Michel Marcus, Aug 04 2025

from functools import reduce
ORsum=lambda l: reduce(int._or_,l,0)
A351995=lambda n,k: ORsum(map(lambda i: (n>>i&1)<<(i*k),range(n.bit_length()))) if k else n.bit_count()
T=lambda n,k: 2*~(~0<A351995(d:=n//(k+1),k)+((r:=n%(k+1))==k or (d&-d)**k*2*(1+2**r-2**k))
#corollary 1:
T=lambda n,k: T(n-(k+1<<(l:=(d:=n//(k+1)).bit_length()-1)),k)|(~(~0<k else int(n==k)
bit=lambda n,k,i: (i%k==n%(k+1) if n%(k+1)>i//k&1) if i else n%(k+1)==k #returns i-th bit of T(n,k)

Let d = floor(n/(k+1)) and m = n mod (k+1), then
T(n,k) = 2 * (2^k-1) * A351995(d,k) + b(n,k) where b(n,k) = 1 if n==k (mod k+1), otherwise b(n,k) = 2*2^(k*val_2(d))*(1+2^m-2^k).
Bounds: 2*(n/(k+1))^k <= T(n,k) <= 2*(2^k-1) * ((n-k)/(k+1))^k+1, with upper equality when n is of form 2^(k*i+1) and lower when n is of form (2^k-1)*2^(k*i+1).
T(n,k) = T(n-(k+1)*2^floor(log_2(d)),k) + 2^(k*floor(log_2(d))+1)*(if d is a power of 2 and m != k then 2^m, else 2^k-1).
O.g.f. for k-th column: 2*(2^k-1) * (Sum_{i>=0} 2^(k*i) * x^((k+1)*2^i) / (1+x^((k+1)*2^i))) / (1-x) + x^k / (1-x^(k+1)) + 2 * ((1-2^k) * (1-x^k)/(1-x) + (1-(2*x)^k)/(1-2*x)) * Sum_{i>=0} 2^(k*i) * x^((k+1)*2^i) / (1-x^((k+1)*2^(i+1))).

A387267 Number of dissections of a convex n-gon into quadrilaterals and pentagons by strictly disjoint diagonals.

Original entry on oeis.org

0, 1, 1, 3, 7, 8, 19, 31, 47, 87, 135, 219, 371, 579, 947, 1535, 2423, 3919, 6239, 9891, 15803, 24987, 39563, 62663, 98751, 155815, 245431, 385771, 606467, 951795, 1492323, 2338703, 3660551, 5725951, 8950543, 13978931, 21820235, 34037067, 53059643, 82670167

Offset: 3

Muhammed Sefa Saydam, Aug 24 2025

Strictly disjoint diagonals means that the diagonals are non-crossing and may not share endpoints.

Muhammed Sefa Saydam, Table of n, a(n) for n = 3..100

Cf. A093128, A159284, A387224.

a(n) = T(n-3) + Sum_{i=1..n-8} T(i)*( T(n-i-4) + T(n-i-7) ) + Sum_{i=n-7..n-5} T(i)*( 1 + T(n-i-4) ) for n >= 9 and T(n) = A159284(n).

A385240 Array read by descending antidiagonals: T(n,k) is the number of k element sets of noncongruent integer sided rectangles that fill an n X n square.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 0, 3, 2, 1, 0, 0, 0, 3, 8, 2, 1, 0, 0, 0, 2, 15, 11, 3, 1, 0, 0, 0, 0, 19, 35, 19, 3, 1, 0, 0, 0, 0, 7, 87, 75, 23, 4, 1, 0, 0, 0, 0, 1, 114, 257, 119, 35, 4, 1, 0, 0, 0, 0, 0, 56, 593, 571, 210, 40, 5, 1, 0

Offset: 1

Janaka Rodrigo, Aug 26 2025

			Array begins:
  1     0     0     0     0
  1     0     0     0     0
  1     1     2     0     0
  1     1     3     3     2
  1     2     8    15    19
  1     2    11    35    87
  1     3    19    75   257
  1     3    23   119   571
  1     4    35   210  1186
  1     4    40   289  2033

Columns: A000012 (k=1), A004526 (k=2), A381847 (k=3), A387171 (k=4), A387241 (k=5).

Cf. A386296 (3-dimensional version).

T(n,1) = 1.

T(n,k) = 0 for k > n^2.

More terms from Sean A. Irvine, Sep 02 2025

A387152 Array read by ascending antidiagonals: A(n, k) = Sum_{j=0..n} binomial(k, j)*|Stirling1(n, j)|.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 1, 2, 1, 0, 2, 3, 3, 1, 0, 6, 7, 6, 4, 1, 0, 24, 23, 16, 10, 5, 1, 0, 120, 98, 57, 30, 15, 6, 1, 0, 720, 514, 257, 115, 50, 21, 7, 1, 0, 5040, 3204, 1407, 546, 205, 77, 28, 8, 1, 0, 40320, 23148, 9076, 3109, 1021, 336, 112, 36, 9, 1

Offset: 0

Peter Luschny, Aug 27 2025

			Array begins:
  [0]  1,     1,      1,      1,       1,       1,       1, ...
  [1]  0,     1,      2,      3,       4,       5,       6, ...
  [2]  0,     1,      3,      6,      10,      15,      21, ...
  [3]  0,     2,      7,     16,      30,      50,      77, ...
  [4]  0,     6,     23,     57,     115,     205,     336, ...
  [5]  0,    24,     98,    257,     546,    1021,    1750, ...
  [6]  0,   120,    514,   1407,    3109,    6030,   10696, ...
  [7]  0,   720,   3204,   9076,   20695,   41330,   75356, ...
  [8]  0,  5040,  23148,  67456,  157865,  323005,  602517, ...
  [9]  0, 40320, 190224, 567836, 1358564, 2837549, 5396650, ...

Rows: A000012 [0], A001477 [1], A000217 [2], A005581 [3], A387204 [4].
Columns: A000007 [0], A000142 [shifted, 1], A387205 [2].
Contains A271700 in transpose.
Cf. A211210 (main diagonal), A130534.

A := (n, k) -> add(binomial(k, j)*abs(Stirling1(n, j)), j = 0..n):
seq(seq(A(n-k, k), k = 0..n), n = 0..10);
# Expanding rows or columns:
RowSer := n -> series((1+x)^k*GAMMA(x + n)/GAMMA(x), x, 12):
Trow := n -> k -> coeff(RowSer(n), x, k):
ColSer := n -> series(orthopoly:-L(n, log(1 - x)), x, 12):
Tcol := k -> n -> n! * coeff(ColSer(k), x, n):
seq(lprint(seq(Trow(n)(k), k = 0..7)), n = 0..9);
seq(lprint(seq(Tcol(k)(n), n = 0..7)), k = 0..9);

from functools import cache
@cache
def T(n: int, k: int) -> int:
    if n == 0: return 1
    if k == 0: return 0
    return (n - 1) * T(n - 1, k) + T(n, k - 1) - (n - 2) * T(n - 1, k - 1)
for n in range(7): print([T(n, k) for k in range(7)])

T(n, k) = n! * [x^n] Laguerre(k, log(1 - x)).
From Natalia L. Skirrow, Aug 27 2025: (Start)
D-finite with T(n,k) = (n-1)*T(n-1,k)+T(n,k-1)-(n-2)*T(n-1,k-1).
O.g.f.: hypergeom([1,y/(1-y)],[],x)/(1-y).
Row o.g.f.: (y/(1-y))_n/(1-y), where (x)_n is the Pochhammer symbol/rising factorial.
Row o.g.f. is also 0^n + y/(1-y)^(n+1)*Prod_{j=1..n-2}(j+1-j*y).
E.g.f.: 1/((1-y)*(1-x)^(y/(1-y))).
Column e.g.f.: hypergeom([-k],[1],log(1-y)).
T(n,k) = [x^k] (1+x)^k*(x)_n.
(End)

A387121 Array read by antidiagonals: T(n,k) is the number of sets of k integer sided cuboids with distinct volumes that fill an n X n X n cube.

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 1, 0, 0, 4, 3, 2, 1, 0, 0, 2, 11, 8, 2, 1, 0, 0, 1, 26, 47, 11, 3, 1, 0, 0, 0, 55, 206, 77, 19, 3, 1, 0, 0, 0, 48, 793, 442, 183, 23, 4, 1, 0, 0, 0, 23, 2653, 2451, 1531, 259, 35, 4, 1, 0, 0, 0, 0, 6706, 13022, 12178

Offset: 1

Janaka Rodrigo, Aug 16 2025

The partitions here must be valid packings of the n X n X n cube, hence T(n,k) is generally less than the number of partitions of n^3 into distinct cuboids (x,y,z) with 1 <= x,y,z <= n and no pair of triplets having equal volume x*y*z.

			Array begins:
  1     0     0     0     0
  1     0     0     0     0
  1     1     2     4     2
  1     1     3    11    26
  1     2     8    47   206
  1     2    11    77   442
  1     3    19   183  1531
  1     3    23   259  2661
  1     4    35   457  5574
  1     4    40   599  8514
  ...

Columns are A004526 (k=2), A381847 (k=3), A385580 (k=4), A387040 (k=5).

T(n,1) = 1, T(n,k) = 0 for k > n^3.

More terms from Sean A. Irvine, Aug 25 2025

A386987 For n >= 2, a(n) is the least r >= 1 such that T(n - r) + ... + T(n - 1) = T(n + 1) + ... + T(n + r) where T(i) is A010060(i).

Original entry on oeis.org

2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3, 4, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 4, 3, 3

Offset: 2

Ctibor O. Zizka, Aug 12 2025

nonn

a(n) is from {1, 2, 3, 4}.

			For n = 6: T(6 - r) + ... + T(5) = T(7) + ... + T(6 + r) is true for the least r = 4  because A010060(2) + A010060(3) + A010060(4) + A010060(5) = A010060(7) + A010060(8) + A010060(9) + A010060(10), thus a(6) = 4.

Cf. A010060, A056196, A079523, A081706, A131323, A225822, A249034.

a[n_] := Module[{s = 0, r = 1}, While[r <= n && (r == 1 || s != 0), s += (ThueMorse[n - r] - ThueMorse[n + r]); r++]; r-1]; Array[a, 100, 2] (* Amiram Eldar, Aug 12 2025 *)

a(A081706(n) + 1) = 1.
a(2*A079523(n)) = 2.
a(A249034(n))= 2.
a(A225822(n)) = 3.
a(A056196(n)) = 3.
a(2*A131323(n)) = 4.
a(2*A249034(n) - 1) = 4.

A386678 Triangle of numerators for rational convergents to Taylor series of Gamma(x+1).

Original entry on oeis.org

1, 1, 0, 1, -1, 5, 1, -17, 1045, -35801, 1, -181, 104905, -38432557, 15859708705, 1, -5197, 82178809, -864396960373, 9983212589988481, -112929359515545345757, 1, -4129, 101866157, -213193733657, 15527707142596399, -138932602159504972471, 2493923095641600267646643, 1

Offset: 0

David Ulgenes, Aug 09 2025

T(n, k) is the numerator of the k-th coefficient in a degree n polynomial approximation to Gamma(x+1) with rational coefficients.

That is, Gamma(x+1) ~ Sum_{j=0..n} A386678(n, j) * x^j / A386679(n, j) which is exact as lim_{n->oo}.

			Let A(n, k) = A386675(n, k)/A386676(n, k) be the triangle
  1;
  1, 0;
  1, 1/4, -1/4;
  1, 17/36, -7/12, 1/9;
  1, 181/288, -167/192, 77/288, -5/192;
  1, 5197/7200, -613/576, 581/1440, -187/2880, 7/1800;
  1, 4129/5400, -60239/51840, 5573/11520, -9877/103680, 1597/172800, -37/103680;
where each successive rows gives better rational approximations to 1/Gamma(x+1). Using the Cauchy product, one can obtain approximations to Gamma(x+1) with this table. For instance, T(3, 2) = -numerator(A(3, 1) * T(3, 1) + A(3, 2) * T(3, 0)) = -numerator(17/36 * (-17/36) + (- 7/12) * 1) = 1045. Doing this for each row yields the full table
  1;
  1, 0;
  1, -1/4, 5/16;
  1, -17/36, 1045/1296, -35801/46656;
  1, -181/288, 104905/82944, -38432557/23887872, 15859708705/6879707136;
As an example, row 3 gives Gamma(x+1) ~ 1 - 17/36x + 1045/1296x^2 - 35801/46656x^3.

Eric Weisstein's World of Mathematics, Cauchy Product.

Cf. A386675, A386676, A386677, A386679.

Table[Numerator@CoefficientList[Series[1/Sum[Sum[LaguerreL[i,1](-1)^i StirlingS1[i,k]/i!,{i,0,m}] x^k,{k,0,m}],{x,0,m}],x],{m,0,10}]

Let A(n, k) be the triangle of coefficients A386675(n, k)/A386676(n, k) (see example).
Then T(0, 0) = 1, and for n>=1, T(n, k) = -numerator(Sum_{j=1..k} A(n, j) * T(n, k-j)). This follows immediately from the Cauchy product applied to (1/f(x)) * f(x) = 1.
T(n, k) is also the k-th coefficient in the Taylor series of 1/(Sum_{j=0..n} A(n, j) * x^j).
Equivalently T(n, k) is the k-th coefficient in the polynomial division 1/(Sum_{j=0..n} A(n, j) * x^j).

A386679 Triangle of denominators for rational convergents to Taylor series of Gamma(x+1).

Original entry on oeis.org

1, 1, 1, 1, 4, 16, 1, 36, 1296, 46656, 1, 288, 82944, 23887872, 6879707136, 1, 7200, 51840000, 373248000000, 2687385600000000, 19349176320000000000, 1, 5400, 58320000, 78732000000, 3401222400000000, 18366600960000000000, 198359290368000000000000, 1, 264600, 140026320000, 9262741068000000, 19607370292742400000000

Offset: 0

David Ulgenes, Aug 09 2025

T(n, k) is the denominator of the k-th coefficient in a degree n polynomial approximation to Gamma(x+1) with rational coefficients.

That is, Gamma(x+1) ~ Sum_{j=0..n} A386678(n, j) * x^j / A386679(n, j) which is exact as lim_{n->oo}.

			Let A(n, k) = A386675(n, k)/A386676(n, k) be the triangle
  1;
  1, 0;
  1, 1/4, -1/4;
  1, 17/36, -7/12, 1/9;
  1, 181/288, -167/192, 77/288, -5/192;
  1, 5197/7200, -613/576, 581/1440, -187/2880, 7/1800;
  1, 4129/5400, -60239/51840, 5573/11520, -9877/103680, 1597/172800, -37/103680;
where each successive rows gives better rational approximations to 1/Gamma(x+1). Using the Cauchy product, one can obtain approximations to Gamma(x+1) with this table. For instance, T(3, 2) = -denominator(A(3, 1) * T(3, 1) + A(3, 2) * T(3, 0)) = -numerator(17/36 * (-17/36) + (- 7/12) * 1) = 1296. Doing this for each row yields the full table:
  1;
  1, 0;
  1, -1/4, 5/16;
  1, -17/36, 1045/1296, -35801/46656;
  1, -181/288, 104905/82944, -38432557/23887872, 15859708705/6879707136; ...
As an example, row 3 gives Gamma(x+1) ~ 1 - 17/36x + 1045/1296x^2 - 35801/46656x^3.

Eric Weisstein's World of Mathematics, Cauchy Product.

Cf. A386675, A386676, A386677, A386678.

Table[Numerator@CoefficientList[Series[1/Sum[Sum[LaguerreL[i,1](-1)^i StirlingS1[i,k]/i!,{i,0,m}] x^k,{k,0,m}],{x,0,m}],x],{m,0,10}]

Let A(n, k) be the triangle of coefficients A386675(n, k)/A386676(n, k) (see example).
Then T(0, 0) = 1, and for n>=1, T(n, k) = -denominator(Sum_{j=1..k} A(n, j) * T(n, k-j)). This follows immediately from the Cauchy product applied to (1/f(x)) * f(x) = 1.
T(n, k) is also the denominator of the k-th coefficient in the Taylor series of 1/(Sum_{j=0..n} A(n, j) * x^j).
Equivalently, T(n, k) is the denominator of the k-th coefficient in the polynomial division 1/(Sum_{j=0..n} A(n, j) * x^j).

A385959 a(0) = 1; a(n) = a(n-1)*(b(n)+1)/(b(n)-1), where b(n) = A385958(n) is the largest prime p such that a(n) is an integer.

Original entry on oeis.org

1, 2, 3, 4, 6, 7, 14, 15, 16, 18, 19, 38, 57, 76, 114, 115, 120, 121, 132, 135, 136, 138, 139, 278, 279, 310, 312, 314, 471, 628, 942, 1099, 2198, 2199, 2932, 4398, 5131, 10262, 10995, 10996, 16494, 19243, 38486, 41235, 41236, 41358, 41471, 41838, 41841, 46490, 55788, 55789, 111578, 167367, 168554, 252831, 252832, 252864

Offset: 0

Thomas Ordowski, Jul 13 2025

a(0) = 1; a(n) is the smallest k such that (k + a(n-1))/(k - a(n-1)) is a prime (A385958).

Note that a(n-1)+1 <= a(n) <= 2*a(n-1).

Martin Fuller, Table of n, a(n) for n = 0..3460

Cf. A385958.

a(n) = Product_{k=1..n} (b(k)+1)/(b(k)-1), where b(n) = A385958(n).

a(n) = (1+t(n))/(1-t(n)) with t(n) = tanh(Sum_{k=1..n} arctanh(1/b(k))).

More terms from Morné Louw and Martin Fuller, Jul 15 2025

cp's OEIS Frontend

User: , 0|1] = t[n

A386822 Irregular table T(n,k) = Product_{j = 1..k} prime(j)^(n-j+1), n >= 0, k = 1..n.

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A385674 Triangle read by rows: T(n,n) = 1 and T(n,k) = (T(n-1,k) | T(n-2,k) | ... | T(n-k,k)) + 1, where | is bitwise OR, (0<=k<=n).

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A387267 Number of dissections of a convex n-gon into quadrilaterals and pentagons by strictly disjoint diagonals.

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A385240 Array read by descending antidiagonals: T(n,k) is the number of k element sets of noncongruent integer sided rectangles that fill an n X n square.

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A387152 Array read by ascending antidiagonals: A(n, k) = Sum_{j=0..n} binomial(k, j)*|Stirling1(n, j)|.

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A387121 Array read by antidiagonals: T(n,k) is the number of sets of k integer sided cuboids with distinct volumes that fill an n X n X n cube.

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A386987 For n >= 2, a(n) is the least r >= 1 such that T(n - r) + ... + T(n - 1) = T(n + 1) + ... + T(n + r) where T(i) is A010060(i).

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A386678 Triangle of numerators for rational convergents to Taylor series of Gamma(x+1).

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