# Problem 238: Infinite string tour
Create a sequence of numbers using the "Blum Blum Shub" pseudo-random
number generator: s0 = 14025256 sn+1 = sn2 mod 20300713 Concatenate
these numbers  s0s1s2… to create a string w of infinite length. Then,
w = 14025256741014958470038053646… For a positive integer k, if no
substring of w exists with a sum of digits equal to k, p(k) is defined
to be zero. If at least one substring of w exists with a sum of digits
equal to k, we define p(k) = z, where z is the starting position of the
earliest such substring. For instance: The substrings 1, 14, 1402, …
with respective sums of digits equal to 1, 5, 7, … start at position 1,
hence p(1) = p(5) = p(7) = … = 1. The substrings 4, 402, 4025, … with
respective sums of digits equal to 4, 6, 11, … start at position 2,
hence p(4) = p(6) = p(11) = … = 2. The substrings 02, 0252, … with
respective sums of digits equal to 2, 9, … start at position 3, hence
p(2) = p(9) = … = 3. Note that substring 025 starting at position 3, has
a sum of digits equal to 7, but there was an earlier substring (starting
at position 1) with a sum of digits equal to 7, so p(7) = 1, not 3. We
can verify that, for 0 < k ≤ 103, ∑ p(k) = 4742. Find ∑ p(k), for
0 < k ≤ 2·1015.