A230956 -id:A230956 - cp's OEIS frontend

A000747 Boustrophedon transform of primes.

2, 5, 13, 35, 103, 345, 1325, 5911, 30067, 172237, 1096319, 7677155, 58648421, 485377457, 4326008691, 41310343279, 420783672791, 4553946567241, 52184383350787, 631210595896453, 8036822912123765, 107444407853010597, 1504827158220643895, 22034062627659931905

Offset: 0

N. J. A. Sloane

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 0..400
Peter Luschny, An old operation on sequences: the Seidel transform.
J. Millar, N. J. A. Sloane, and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54 (Abstract, pdf, ps).
J. Millar, N. J. A. Sloane, and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory Ser. A, 76(1) (1996), 44-54.
Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [USA access only through the HATHI TRUST Digital Library]
Ludwig Seidel, Über eine einfache Entstehungsweise der Bernoulli'schen Zahlen und einiger verwandten Reihen, Sitzungsberichte der mathematisch-physikalischen Classe der königlich bayerischen Akademie der Wissenschaften zu München, volume 7 (1877), 157-187. [Access through ZOBODAT]
N. J. A. Sloane, Transforms.
Wikipedia, Boustrophedon transform.
Index entries for sequences related to boustrophedon transform

Cf. A000040, A109449, A230953, A230956, A230954, A230955.

a000747 n = sum $ zipWith (*) (a109449_row n) a000040_list
-- Reinhard Zumkeller, Nov 03 2013

t[n_, 0] := Prime[n+1]; t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k]; a[n_] := t[n, n]; Array[a, 30, 0] (* Jean-François Alcover, Feb 12 2016 *)

from itertools import islice, count, accumulate
from sympy import prime
def A000747_gen(): # generator of terms
    blist = tuple()
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist),initial=prime(i))))[-1]
A000747_list = list(islice(A000747_gen(),30)) # Chai Wah Wu, Jun 11 2022

a(n) = Sum_{k=0..n} A109449(n,k)*A000040(k+1). - Reinhard Zumkeller, Nov 03 2013

E.g.f.: (sec(x) + tan(x)) * Sum_{k>=0} prime(k+1)*x^k/k!. - Ilya Gutkovskiy, Jun 26 2018

A230953 Boustrophedon transform of odd primes, cf. A065091.

Original entry on oeis.org

3, 8, 20, 53, 154, 505, 1944, 8651, 44046, 252271, 1605874, 11245261, 85907084, 710970323, 6336648426, 60510526207, 616355168958, 6670526004559, 76438597647616, 924584128977111, 11772170758462928, 157382330019694067, 2204239468545788024, 32275035859881159165

Offset: 0

Reinhard Zumkeller, Nov 03 2013

nonn

Reinhard Zumkeller, Table of n, a(n) for n = 0..400
Peter Luschny, An old operation on sequences: the Seidel transform
J. Millar, N. J. A. Sloane and N. E. Young, A new operation on sequences: the Boustrophedon transform, J. Combin. Theory, 17A 44-54 1996 (Abstract, pdf, ps).
Wikipedia, Boustrophedon transform
Index entries for sequences related to boustrophedon transform

Cf. A000747, A230956, A230954, A230955.

a230953 n = sum $ zipWith (*) (a109449_row n) $ tail a000040_list

t[n_, 0] := Prime[n+2]; t[n_, k_] := t[n, k] = t[n, k-1] + t[n-1, n-k]; a[n_] := t[n, n]; Array[a, 30, 0] (* Jean-François Alcover, Feb 12 2016 *)

from itertools import accumulate, count, islice
from sympy import prime
def A230953_gen(): # generator of terms
    blist = tuple()
    for i in count(2):
        yield (blist := tuple(accumulate(reversed(blist),initial=prime(i))))[-1]
A230953_list = list(islice(A230953_gen(),40)) # Chai Wah Wu, Jun 12 2022

a(n) = Sum_{k=0..n} A109449(n,k)*A000040(k+2).

E.g.f.: (sec(x) + tan(x)) * Sum_{k>=0} prime(k+2)*x^k/k!. - Ilya Gutkovskiy, Jun 26 2018

cp's OEIS Frontend

A000747 Boustrophedon transform of primes.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

Python

Formula