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<p>Create Project Euler/238 - Infinite String Tour (via create-page on MediaWiki MCP Server)</p> <p><b>New page</b></p><div>==Problem Statement==<br /> <br /> &#039;&#039;&#039;Infinite String Tour&#039;&#039;&#039;<br /> <br /> Create a sequence of numbers using the &quot;Blum Blum Shub&quot; pseudo-random number generator:<br /> <br /> s_0 = 14025256<br /> s_{n+1} = s_n^2 mod 20300713<br /> <br /> Concatenate these numbers s_0 s_1 s_2 … to create a string w of infinite length. Then, w = 14025256741014958470038053646…<br /> <br /> 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.<br /> <br /> For instance:<br /> * 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.<br /> * 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.<br /> * The substrings 02, 0252, … with respective sums of digits equal to 2, 9, … start at position 3, hence p(2) = p(9) = … = 3.<br /> <br /> 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.<br /> <br /> We can verify that, for 0 &lt; k ≤ 10^3, ∑ p(k) = 4742.<br /> <br /> Find ∑ p(k), for 0 &lt; k ≤ 2·10^15.<br /> <br /> ==Flags==<br /> <br /> {{ProjectEulerFlag}}</div>

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