,6, has authored 2 sequences.
A354157
Numerator of generalized Catalan number c_3(n) (see Comments).
Original entry on oeis.org
1, 1, 5, 104, 836, 7315, 202895, 1949900, 19284511, 1754890501, 18058389349, 188502545504, 5973492827120, 63732573470888, 685813307216632, 22303841469480032, 243350841747362492, 2670252449037801100, 265034693078133749180, 2936064912067020698720
Offset: 0
The first few c_3(n) are 1, 1/3, 5/9, 104/81, 836/243, 7315/729, 202895/6561, 1949900/19683, 19284511/59049, 1754890501/1594323, 18058389349/4782969, ...
- J. B. Cosgrave, A Mersenne-Wieferich Odyssey, Manuscript, May 2022. See Section 18.6.
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c := proc(n) 1/3 * 1/(n+1/3) * mul(n + i + 1/3, i = 0..(n-1))/n!: end;
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c3[n_] := With[{k = 3}, Pochhammer[n+1+1/k, n-1]/(k*n!)];
Table[Numerator[c3[n]], {n, 1, 19}] (* Jean-François Alcover, Apr 14 2023 *)
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a(n) = numerator((1/3)*(1/(n+1/3))*prod(i=0, n-1, n+i+1/3)/n!) \\ Rémy Sigrist, May 30 2022
A330339
Boustrophedon primes: write the numbers 0, 1, 2, 3, ... in a triangle on a square grid in the boustrophedon manner, ending a row when a prime is reached; sequence lists primes that appear in the zeroth column.
Original entry on oeis.org
37, 53, 89, 113, 3821, 3989, 4657, 28661, 29021, 41641, 41669, 44249, 50909, 56053, 57041, 57301, 133981, 16501361, 46178761, 47633441, 47633477, 47722049, 47736121, 47774621, 47803477, 47810209, 47835013, 47835341, 47854969, 47862413, 47865017, 49448573, 49448617
Offset: 1
- Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 516 terms from Hans Havermann)
- Eric Angelini, Illustration of beginning of the triangle in A330339.
- Hans Havermann, Plot of 4*10^8 terms of A330545, sampled every 1000 terms, points joined.
- Hans Havermann, More detailed view of terms of A330545 from 290 million to 310 million, sampled every 10 terms, points joined.
- N. J. A. Sloane, Illustration of first 16 rows of A330545.
- N. J. A. Sloane, Notes on the sequence of Bostrophedon primes (A330339) and the "ski-run" A330545.
- N. J. A. Sloane, State diagram for columns of A330545.
- Walter Trump, An extended picture of the triangle in A330339, showing the first 550 rows, down to the row that starts 3989. [The zeroth column is just to the right of the vertical red line. Note that after a while the rows extend to the left of the red line. The digits are too small to be read.]
- Walter Trump, An extended picture of the triangle in A330339, showing the first 550 rows, down to the row that starts 3989. [Same picture as the previous one, but with 6 red dots added to show the primes in column 0.]
A330546 gives the list of indices i such that a(n) = prime(i).
A127596 is another sequence with a similar flavor.
Not to be confused with
A000747 = Boustrophedon transform of primes.
Comments