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id	title	challengeType	forumTopicId	dashedName
5900f45b1000cf542c50ff6d	Problem 238: Infinite string tour	5	301883	problem-238-infinite-string-tour

--description--

Create a sequence of numbers using the "Blum Blum Shub" pseudo-random number generator:


s_0 = 14025256 \\\\
s_{n + 1} = {s_n}^2 \\; mod \\; 20\\,300\\,713

Concatenate these numbers s_0s_1s_2\ldots to create a string w of infinite length. Then, w = 14025256741014958470038053646\ldots

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) = \ldots = 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) = \ldots = 2.

The substrings 02, 0252, … with respective sums of digits equal to 2, 9, … start at position 3, hence p(2) = p(9) = \ldots = 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 ≤ {10}^3, \sum p(k) = 4742.

Find \sum p(k), for 0 < k ≤ 2 \times {10}^{15}.

--hints--

infiniteStringTour() should return 9922545104535660.

assert.strictEqual(infiniteStringTour(), 9922545104535660);

--seed--

--seed-contents--

function infiniteStringTour() {

  return true;
}

infiniteStringTour();

--solutions--

// solution required

1.8 KiB Raw Blame History