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A230953
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Boustrophedon transform of odd primes, cf. A065091.
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7
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3, 8, 20, 53, 154, 505, 1944, 8651, 44046, 252271, 1605874, 11245261, 85907084, 710970323, 6336648426, 60510526207, 616355168958, 6670526004559, 76438597647616, 924584128977111, 11772170758462928, 157382330019694067, 2204239468545788024, 32275035859881159165
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refs;
listen;
history;
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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, 17A 44-54 1996 (Abstract, pdf, ps).
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+2).
E.g.f.: (sec(x) + tan(x)) * Sum_{k>=0} prime(k+2)*x^k/k!. - Ilya Gutkovskiy, Jun 26 2018
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MATHEMATICA
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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 *)
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PROG
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(Haskell)
a230953 n = sum $ zipWith (*) (a109449_row n) $ tail a000040_list
(Python)
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
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CROSSREFS
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Cf. A000747, A230956, A230954, A230955.
Sequence in context: A027220 A305823 A333679 * A026995 A018035 A271843
Adjacent sequences: A230950 A230951 A230952 * A230954 A230955 A230956
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KEYWORD
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nonn
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AUTHOR
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Reinhard Zumkeller, Nov 03 2013
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STATUS
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approved
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