Questions tagged [digit-sequences]

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9
votes
4answers
1k views

Determining occurrence of a sequence of numbers in the first 50,000 primes

I have to determine how many of the first 50,000 prime numbers (digits) contain the sequence 5, 4, 3, in that order. The numbers don't have to necessarily be consecutive. For example, 566453 is a ...
1
vote
1answer
21 views

Can FindSequenceFunction work on subscripts/superscripts?

I am trying to find a pattern 'encoded' into variables with superscript labels, which incidentally look much like exponents. FindSequenceFunction though doesn't ...
1
vote
2answers
87 views

Short Normal Numbers in base 10

Normal numbers in base 10 are those for which, in the base 10 decimal expansion, you can find every natural number. Champernowne's number is a very simple example of this where it is simply written as:...
2
votes
2answers
62 views

Counting the number of Configurations in an Array with Constraints

Consider an array $$\{a_i\}, i=1, ..., N$$ with periodic boundary condition, i.e. $i\equiv i+N$. $a_i\in \{0, 1\}$. I would like to count the number of configurations of the array $\{a_i\}$ satisfying ...
1
vote
2answers
130 views

Listing all monotone binary functions

A monotone binary function is defined as follows: Given binary vectors $\bf x$ and $\bf y$ (each having $n$ bits) with $\bf x\geq \bf y$, a function $f:\bf x\rightarrow\{0,1\}$ is called monotone if $...
4
votes
1answer
169 views

Self-locating Strings in $\pi$?

According to The Pi-Search Page, in the first 100 million digits of $\pi$ the following numbers are self-locating: 1, 16470, 44899, 79873884. The following inefficient code (which also does not ...