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

Author

Pontus von Brömssen, Oct 24 2020

Keywords

• sign

Links

• Eric Weisstein's World of Mathematics, Boustrophedon Transform
• Wikipedia, Boustrophedon transform
• Index entries for sequences related to boustrophedon transform

Crossrefs

Cf. A000040, A000111, A000747.

Programs

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

Formula

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