A376603 Points of nonzero curvature in the sequence of composite numbers (A002808).

2, 4, 6, 8, 10, 12, 13, 17, 19, 23, 24, 26, 28, 30, 31, 35, 36, 40, 42, 46, 47, 49, 51, 55, 56, 58, 59, 63, 64, 70, 71, 73, 75, 77, 79, 81, 82, 94, 95, 97, 98, 102, 104, 112, 114, 118, 119, 123, 124, 126, 127, 131, 132, 136, 138, 146, 148, 150, 152, 162, 163

Offset

1,1

Comments

These are points at which the second differences (A073445) are nonzero.

Links

Dominic McCarty, Table of n, a(n) for n = 1..1000

Gus Wiseman, Points of nonzero curvature in the sequence of composite numbers.

Example

The composite numbers (A002808) are:
  4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, ...
with first differences (A073783):
  2, 2, 1, 1, 2, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 2, 1, 1, 2, ...
with first differences (A073445):
  0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, -1, 0, 0, 0, 1, 0, -1, 0, 0, 0, 1, -1, 0, ...
with nonzero terms at (A376603):
  2, 4, 6, 8, 10, 12, 13, 17, 19, 23, 24, 26, 28, 30, 31, 35, 36, 40, 42, 46, 47, ...

Mathematica

Join@@Position[Sign[Differences[Select[Range[100], CompositeQ], 2]], 1|-1]

Crossrefs

Partitions into composite numbers are counted by A023895, factorizations A050370.

These are the positions of nonzero terms in A073445.

For first differences we had A073783, ones A375929, complement A065890.

For prime instead of composite we have A333214.

The complement is A376602.

For upward concavity (instead of nonzero) we have A376651, downward A376652.

For composite numbers: A002808 (terms), A073783 (first differences), A073445 (second differences), A376602 (zeros), A376651 (concave-up), A376652 (concave-down).

For nonzero curvature: A333214 (prime), A376589 (non-perfect-power), A376592 (squarefree), A376595 (nonsquarefree), A376598 (prime-power), A376601 (non-prime-power).

Cf. A000961, A064113, A246655, A251092, A258025, A333254.

Sequence in context: A356066 A285591 A327210 * A274611 A319808 A055956

Adjacent sequences: A376600 A376601 A376602 * A376604 A376605 A376606

Keyword

nonn

Author

Gus Wiseman, Oct 05 2024

Status

approved