oeis_a337724_sum_with_rounding.rb

require 'prime'
PRIMES = Prime.first(1000)

# Kevin Ryde pointed out that A337724 corresponds to this formula, with crazy rounding
# prime(n) - prime(n-2)/2 + prime(n-4)/2^2 - prime(n-6)/2^3 + ...
values = [0, 1]
30.times do |i|
    sum = 0
    power = 0
    sign = 1
    j = i
    while j >= 0
        prime = PRIMES[j]
        sum += sign * prime.to_f / (2**power)
        power += 1
        sign = -sign
        j -= 2
    end
    values << sum.round.to_i
end
p values

# Program output:
# [0, 1, 2, 3, 4, 6, 9, 10, 13, 14, 17, 22, 23, 26, 30, 30, 32, 38, 43, 42, 46, 50, 50, 54, 58, 62, 68, 70, 69, 72, 75, 77]