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A000747
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Boustrophedon transform of primes.
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8
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2, 5, 13, 35, 103, 345, 1325, 5911, 30067, 172237, 1096319, 7677155, 58648421, 485377457, 4326008691, 41310343279, 420783672791, 4553946567241, 52184383350787, 631210595896453, 8036822912123765, 107444407853010597
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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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
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a000747 n = sum $ zipWith (*) (a109449_row n) a000040_list
-- Reinhard Zumkeller, Nov 03 2013
(Python)
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
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CROSSREFS
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Cf. A000040, A109449, A230953, A230956, A230954, A230955.
Sequence in context: A131868 A339294 A272064 * A151259 A149853 A148291
Adjacent sequences: A000744 A000745 A000746 * A000748 A000749 A000750
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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