The following puzzle was invented by Eric Angelini in September 2007.
As mentioned in A131744 :
the sequence is defined by the property that if one writes the English names for the entries, replaces each letter with its rank in the alphabet and calculates the absolute values of the differences, one recovers the sequence.
To be precise, the alphabet starts at 1, so a is 1, b is 2, etc. Also, 15 is supposed to be treated as fifteen and 21 as twentyone (not twenty-one).
Begin with 1 :
1 -> "one" -> 15,14,5 -> absolute(15-14),absolute(14-5) -> 1,9 1,9 -> "one,nine" -> 15,14,5,14,9,14,5 -> 1,9,9,5,5,9 1,9,9,5,5,9 -> "one,nine,nine,five,five,nine" -> 15,14,5,14,9,14,5,14,9,14,5,6,9,22,5,6,9,22,5,14,9,14,5 -> 1,9,9,5,5,9,9,5,5,9,1,3,13,17,1,3,13,17,9,5,5,9 1,9,9,5,5,9,9,5,5,9,1,3,13,17,1,3,13,17,9,5,5,9 -> ...
So the first 22 terms are :
You can find the 40000 first terms here : b131744
Sequence I/O methods apply. You may use one of the following I/O methods:
- Take no input and output the sequence indefinitely,
- Take a (0- or 1-based) index i and output the i-th term,
- Take a non-negative integer i and output the first i terms.
The shortest code in bytes wins.