A376266 Sorted positions of first appearances in A376264 (run-sums of first differences of nonsquarefree numbers).

1, 2, 3, 8, 10, 14, 18, 53, 1437, 6222, 40874

Offset: 1

Author

Gus Wiseman, Sep 27 2024

Keywords

• nonn
• more

Examples

			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, ...
		

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.

Cf. A037201, A053797, A053806, A120992, A373197, A373198, A373413, A373822, A375707, A376306, A376307, A376521.

Programs

Mathematica

q=Total/@Split[Differences[Select[Range[10000], !SquareFreeQ[#]&]]]//Most;
Select[Range[Length[q]],!MemberQ[Take[q,#-1],q[[#]]]&]