A338398 Inverse boustrophedon transform of the primes.

2, 1, 1, -3, -1, -29, 33, -315, 1251, -7905, 48667, -344723, 2623549, -21739937, 193680399, -1849767375, 18840708855, -203907377005, 2336594492591, -28262970918841, 359855118160333, -4810909461068941, 67379837645787507, -986592769520379701

Offset

0,1

Links

Table of n, a(n) for n=0..23.

Eric Weisstein's World of Mathematics, Boustrophedon Transform

Wikipedia, Boustrophedon transform

Index entries for sequences related to boustrophedon transform

Formula

a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n,k) * A000111(n-k) * A000040(k+1).

Prog

(Python)
import sympy
def A338398(n):
  T=[]
  for k in range(n+1):
    T.append(sympy.prime(k+1))
    T.reverse()
    for i in range(k):
      T[i+1]=T[i]-T[i+1]
  return T[-1]
(Python)
from itertools import accumulate, islice, count
from operator import sub
from sympy import prime
def A338398_gen(): # generator of terms
    blist = tuple()
    for i in count(1):
        yield (blist := tuple(accumulate(reversed(blist), func=sub, initial=prime(i))))[-1]
A338398_list = list(islice(A338398_gen(), 20)) # Chai Wah Wu, Jun 10 2022

Crossrefs

Cf. A000040, A000111, A000747.

Sequence in context: A318833 A173937 A046223 * A192181 A073463 A183568

Adjacent sequences: A338395 A338396 A338397 * A338399 A338400 A338401

Keyword

sign

Author

Pontus von Brömssen, Oct 24 2020

Status

approved