OFFSET
1,2
COMMENTS
The prime numbers are (A000040):
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, ...
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, ...
with first differences (A036263):
1, 0, 2, -2, 2, -2, 2, 2, -4, 4, -2, -2, 2, 2, 0, -4, 4, -2, -2, 4, -2, 2, 2, ...
with sorted first appearances at (A376656):
1, 2, 3, 4, 9, 10, 29, 30, 33, 34, 96, 98, 99, 154, 179, 180, 189, 216, 217, ...
MATHEMATICA
q=Differences[Select[Range[1000], PrimeQ], 2];
Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&]
CROSSREFS
These are the sorted positions of first appearances in A036263.
For first differences we had A373400(n) + 1, except initial terms.
A333254 lists run-lengths of differences between consecutive primes.
KEYWORD
nonn
AUTHOR
Gus Wiseman, Oct 07 2024
STATUS
approved