OFFSET
1,2
COMMENTS
Also the run-compression of the sequence of first differences of prime numbers, where we define the run-compression of a sequence to be the anti-run obtained by reducing each run of repeated parts to a single part. Alternatively, we can remove all parts equal to the part immediately to their left. For example, (1,1,2,2,1) has run-compression (1,2,1). - Gus Wiseman, Sep 16 2024
LINKS
Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
FORMULA
a(n>1) = 2*A373947(n-1). - Gus Wiseman, Sep 16 2024
MATHEMATICA
Flatten[Split[Differences[Prime[Range[150]]]]/.{(k_)..}:>k] (* based on a program by Harvey P. Dale, Jun 21 2012 *)
PROG
(Haskell)
a037201 n = a037201_list !! (n-1)
a037201_list = f a001223_list where
f (x:xs@(x':_)) | x == x' = f xs
| otherwise = x : f xs
-- Reinhard Zumkeller, Feb 27 2012
(PARI) t=0; p=2; forprime(q=3, 1e3, if(q-p!=t, print1(q-p", ")); t=q-p; p=q) \\ Charles R Greathouse IV, Feb 27 2012
CROSSREFS
The repeats were at positions A064113 before being omitted.
Adding up runs instead of compressing them gives A373822.
The even terms halved are A373947.
For prime-powers instead of prime numbers we have A376308.
A003242 counts compressed compositions.
A333254 lists run-lengths of differences between consecutive primes.
A373948 encodes compression using compositions in standard order.
KEYWORD
easy,nonn,nice
AUTHOR
EXTENSIONS
Offset corrected by Reinhard Zumkeller, Feb 27 2012
STATUS
approved