Comparision of a136437 and a338530

a136437_a338530_compare.rb

# Regarding
# https://oeis.org/draft/A338530
# https://oeis.org/A136437
#
# Hugo Pfoertner: Can you please check the relation to A136437? It seems that (a(n)+2)/2 = (A136437-1)/2 for the even terms after a(31).
# Hugo Pfoertner: I checked against A136437 and found a(n)=A136437(n)-3 for 31<=n<=128.
#
# Here is output of the two sequences A136437 and A338530. They are indeed the same for this range.
#
require 'prime'

# https://oeis.org/A136437
def a136437(count)
    values = []
    Prime.first(count).each do |prime|
        k, v = 1, 1
        (k += 1; v *= k) while (k + 1) * v <= prime
        values << prime - v
    end
    values
end

# https://oeis.org/draft/A338530
def a338530(count)
    primes = Prime.first(count)
    values = [1]
    (count-1).times { |n| values << (primes[n+1] + values[-1]) % primes[n] }
    values
end

values0 = a136437(128).drop(30)
puts "A136437 #{values0}"

values1 = a338530(128).drop(30).map { |v| v + 3 }
puts "\nA338530 #{values1}"

raise "the values are different" if values0 != values1

puts "\nThe values are identical."

=begin

PROGRAM OUTPUT IS HERE:

A136437 [7, 11, 17, 19, 29, 31, 37, 43, 47, 53, 59, 61, 71, 73, 77, 79, 91, 103, 107, 109, 113, 119, 121, 131, 137, 143, 149, 151, 157, 161, 163, 173, 187, 191, 193, 197, 211, 217, 227, 229, 233, 239, 247, 253, 259, 263, 269, 277, 281, 289, 299, 301, 311, 313, 319, 323, 329, 337, 341, 343, 347, 359, 367, 371, 379, 383, 389, 401, 403, 421, 427, 437, 443, 449, 451, 457, 467, 473, 479, 481, 487, 493, 497, 499, 511, 521, 523, 527, 533, 539, 541, 553, 557, 563, 571, 581, 589, 599]

A338530 [7, 11, 17, 19, 29, 31, 37, 43, 47, 53, 59, 61, 71, 73, 77, 79, 91, 103, 107, 109, 113, 119, 121, 131, 137, 143, 149, 151, 157, 161, 163, 173, 187, 191, 193, 197, 211, 217, 227, 229, 233, 239, 247, 253, 259, 263, 269, 277, 281, 289, 299, 301, 311, 313, 319, 323, 329, 337, 341, 343, 347, 359, 367, 371, 379, 383, 389, 401, 403, 421, 427, 437, 443, 449, 451, 457, 467, 473, 479, 481, 487, 493, 497, 499, 511, 521, 523, 527, 533, 539, 541, 553, 557, 563, 571, 581, 589, 599]

The values are identical.

=end