oeis_a337723_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 + ...
# What about A337723, does it have a similar formula, with crazy rounding?
# Yes, I think I have found a formula that can do it.

accumulator_a = 0.5
accumulator_b = 1
values = [0, 1]
bias = 0.5
28.times do |i|
    sum = 0
    prime = PRIMES[i]
    if i.even?
        accumulator_a = prime - ((bias + accumulator_a) / 2.0)
        sum = accumulator_a
    else
        accumulator_b = prime - ((bias + accumulator_b) / 2.0)
        sum = accumulator_b
    end
    values << sum.round.to_i
end
p values

# Program output:
# [0, 1, 2, 2, 4, 6, 9, 10, 12, 14, 17, 22, 22, 26, 30, 30, 32, 38, 43, 42, 45, 50, 50, 54, 58, 62, 68, 70, 69, 72]