A030196 -id:A030196 - cp's OEIS frontend

A049039 Geometric Connell sequence: 1 odd, 2 even, 4 odd, 8 even, ...

1, 2, 4, 5, 7, 9, 11, 12, 14, 16, 18, 20, 22, 24, 26, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 121, 123, 125

Offset: 1

James Sellers

Reinhard Zumkeller, Rows n=1..13 of triangle, flattened
Ralf Stephan, Some divide-and-conquer sequences ...
Ralf Stephan, Table of generating functions

Cf. A337300 (partial sums), A043529 (first differences).
Cf. A001614, A033292, A030196, A000295, A050487, A050488.
Cf. A160464, A160465 and A160473. - Johannes W. Meijer, May 24 2009

a049039 n k = a049039_tabl !! (n-1) !! (k-1)
a049039_row n = a049039_tabl !! (n-1)
a049039_tabl = f 1 1 [1..] where
   f k p xs = ys : f (2 * k) (1 - p) (dropWhile (<= last ys) xs) where
     ys  = take k $ filter ((== p) . (`mod` 2)) xs
-- Reinhard Zumkeller, Jan 18 2012, Jul 08 2011

Digits := 100: [seq(2*n-1-floor(evalf(log(n)/log(2))), n=1..100)];

a[0] = 0; a[n_?EvenQ] := a[n] = a[n/2]+n-1; a[n_?OddQ] := a[n] = a[(n-1)/2]+n; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Dec 27 2011, after Ralf Stephan *)

a(n) = n<<1 - 1 - logint(n,2); \\ Kevin Ryde, Feb 12 2022

def A049039(n): return (n<<1)-n.bit_length() # Chai Wah Wu, Aug 01 2022

a(n) = 2n - 1 - floor(log_2(n)).
a(2^n-1) = 2^(n+1) - (n+2) = A000295(n+1), the Eulerian numbers.
a(0)=0, a(2n) = a(n) + 2n - 1, a(2n+1) = a(n) + 2n + 1. - Ralf Stephan, Oct 11 2003

Keyword tabf added by Reinhard Zumkeller, Jan 22 2012

A014630 Distinct elements occurring in triangle of Eulerian numbers (unsorted).

Original entry on oeis.org

1, 4, 11, 26, 66, 57, 302, 120, 1191, 2416, 247, 4293, 15619, 502, 14608, 88234, 156190, 1013, 47840, 455192, 1310354, 2036, 152637, 2203488, 9738114, 15724248, 4083, 478271, 10187685, 66318474, 162512286, 8178, 1479726, 45533450, 423281535, 1505621508, 2275172004

Offset: 1

Mohammad K. Azarian

It appears that no term other than 1 appears on different rows of A008292. If so, row n contains floor((n-1)/2) terms for n >= 2. - Pontus von Brömssen, Jul 20 2024

			As an irregular triangle:
   n\k|     1       2         3          4           5           6
  ----+-----------------------------------------------------------
   1  |     1
   2  |     (no terms)
   3  |     4
   4  |    11
   5  |    26      66
   6  |    57     302
   7  |   120    1191      2416
   8  |   247    4293     15619
   9  |   502   14608     88234     156190
  10  |  1013   47840    455192    1310354
  11  |  2036  152637   2203488    9738114    15724248
  12  |  4083  478271  10187685   66318474   162512286
  13  |  8178 1479726  45533450  423281535  1505621508  2275172004
  14  | 16369 4537314 198410786 2571742175 12843262863 27971176092

Cf. A008292, A030196.

More terms from James Sellers

A065050 Prime numbers in the triangle of Eulerian numbers.

Original entry on oeis.org

11, 1013, 15619, 16369, 65519, 478271, 13824739, 67108837, 1125899906842573, 72057594037927879, 1180591620717411303353, 2153693845981967454679177, 12086992684284175368032851, 22528399544594441658590663774175461

Offset: 1

Henry Bottomley, Nov 06 2001

nonn

			Pairs (n, k) such that Eulerian(n, k) is prime are (4, 2), (10, 2), (8, 4), (14, 2), (16, 2), (12, 3), (15, 3), (26, 2), (50, 2), (56, 2), (70, 2), (51, 3), (27, 9), (72, 3), (116, 2), (87, 3), (183, 3).

Sean A. Irvine, Table of n, a(n) for n = 1..18

Cf. A008292, A030196.

Eulerian(n,k)=sum(j=0,k,(-1)^j*(k-j)^n*binomial(n+1,j));
lista(nn) = {my(list=List()); for (n=1, nn, for (k=1, n, if (ispseudoprime(p=Eulerian(n, k)), listput(list, p)););); Vec(Set(list));} \\ Michel Marcus, May 25 2022

More terms from Randall L Rathbun, Jan 21 2002

cp's OEIS Frontend

A049039 Geometric Connell sequence: 1 odd, 2 even, 4 odd, 8 even, ...

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A014630 Distinct elements occurring in triangle of Eulerian numbers (unsorted).

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A065050 Prime numbers in the triangle of Eulerian numbers.

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