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A376521
Sorted positions of first appearances in the run-compression (A037201) of the first differences (A001223) of the prime numbers (A000040).
4
1, 2, 3, 8, 22, 28, 32, 42, 91, 141, 172, 198, 242, 259, 341, 400, 556, 692, 1119, 1737, 1779, 2072, 2101, 2913, 3126, 3204, 3246, 3457, 3598, 4294, 4383, 7596, 7651, 8284, 11986, 13729, 14220, 15101, 16273, 18217, 22303, 29523, 30243, 32236, 32808, 32820
OFFSET
1,2
COMMENTS
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).
EXAMPLE
The sequence of prime numbers (A000040) is:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, ...
with first differences (A001223):
1, 2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, ...
with run-compression (A037201):
1, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, 2, 4, ...
with first appearances at (A376521):
1, 2, 3, 8, 22, 28, 32, 42, 91, 141, 172, 198, 242, 259, 341, 400, 556, 692, 1119, ...
MATHEMATICA
q=First/@Split[Differences[Select[Range[1000], PrimeQ]]];
Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&]
CROSSREFS
These are the sorted positions of first appearances in A037201.
For positions of twos instead of first appearances we have A376343.
The unsorted version is A376520.
A000040 lists the prime numbers, differences A001223.
A003242 counts compressed compositions, ranks A333489.
A333254 lists run-lengths of differences between consecutive primes.
A373948 encodes compression using compositions in standard order.
Sequence in context: A238329 A272333 A098119 * A376520 A049959 A006545
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 26 2024
STATUS
approved