More precisely: Let's assume that pi is absolutely normal and we use a 256 letters alphabet (ascii, ¿latin-1?).
I'm almost sure that if we have a "book" with N characters, in average, the number of (decimal) digits of the index of that string in pi is N * log(256) / log(10). (I'm too lazy to write the proof now, so perhaps I'm making a mistake.) This is (esencially) equivalent to that the expected position is 256^N. (But I'm taking averages willy-nilly.)
If this is correct, the position increase exponentially with the book length, but the numbers of digits in the position increase linearly.
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More precisely: Let's assume that pi is absolutely normal and we use a 256 letters alphabet (ascii, ¿latin-1?).
I'm almost sure that if we have a "book" with N characters, in average, the number of (decimal) digits of the index of that string in pi is N * log(256) / log(10). (I'm too lazy to write the proof now, so perhaps I'm making a mistake.) This is (esencially) equivalent to that the expected position is 256^N. (But I'm taking averages willy-nilly.)
If this is correct, the position increase exponentially with the book length, but the numbers of digits in the position increase linearly.