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A376266
Sorted positions of first appearances in A376264 (run-sums of first differences of nonsquarefree numbers).
3
1, 2, 3, 8, 10, 14, 18, 53, 1437, 6222, 40874
OFFSET
1,2
EXAMPLE
The sequence of nonsquarefree numbers (A013929) is:
4, 8, 9, 12, 16, 18, 20, 24, 25, 27, 28, 32, 36, 40, 44, 45, 48, 49, 50, ...
with first differences (A078147):
4, 1, 3, 4, 2, 2, 4, 1, 2, 1, 4, 4, 4, 4, 1, 3, 1, 1, 2, 2, 2, 4, 3, 1, ...
with runs:
(4),(1),(3),(4),(2,2),(4),(1),(2),(1),(4,4,4,4),(1),(3),(1,1),(2,2,2), ...
with sums (A376264):
4, 1, 3, 4, 4, 4, 1, 2, 1, 16, 1, 3, 2, 6, 4, 3, 1, 8, 3, 1, 4, 1, 3, 4, 4, ...
with first appearances at (A376266):
1, 2, 3, 8, 10, 14, 18, 53, 1437, 6222, 40874, ...
MATHEMATICA
q=Total/@Split[Differences[Select[Range[10000], !SquareFreeQ[#]&]]]//Most;
Select[Range[Length[q]], !MemberQ[Take[q, #-1], q[[#]]]&]
CROSSREFS
These are the positions of first appearances in A376264.
The unsorted version is A376265.
A000040 lists the prime numbers, differences A001223.
A000961 and A246655 list prime-powers, differences A057820.
A005117 lists squarefree numbers, differences A076259 (ones A375927).
A013929 lists nonsquarefree numbers, differences A078147.
A333254 lists run-lengths of differences between consecutive primes.
A376267 gives run-lengths of first differences of nonsquarefree numbers.
A376312 gives run-compression of first differences of nonsquarefree numbers.
A376305 gives run-compression of differences of squarefree numbers, ones A376342.
Sequence in context: A281929 A286092 A100317 * A295030 A317655 A060697
KEYWORD
nonn,more
AUTHOR
Gus Wiseman, Sep 27 2024
STATUS
approved