A377037 Position of first zero in the n-th differences of the composite numbers (A002808), or 0 if it does not appear.

1, 14, 2, 65, 1, 83, 2, 7, 1, 83, 2, 424, 12, 32, 11, 733, 10, 940, 9, 1110, 8, 1110, 7, 1110, 6, 1110, 112, 1110, 111, 1110, 110, 2192, 109, 13852, 108, 13852, 107, 13852, 106, 13852, 105, 17384, 104, 17384, 103, 17384, 102, 17384, 101, 27144, 552, 28012, 551

Offset: 2

Author

Gus Wiseman, Oct 17 2024

Keywords

• nonn

Examples

			The third differences of the composite numbers are:
  -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -2, 1, 0, 0, 1, -1, -1, ...
so a(3) = 14.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..100

Crossrefs

The version for prime instead of composite is A376678.

For noncomposite numbers we have A376855.

This is the first position of 0 in row n of the array A377033.

For squarefree instead of composite we have A377042, nonsquarefree A377050.

For prime-power instead of composite we have A377055.

Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).

A000040 lists the primes, differences A001223, second A036263.

A002808 lists the composite numbers, differences A073783, second A073445.

A008578 lists the noncomposites, differences A075526.

A377036 gives first term of the n-th differences of the composite numbers, for primes A007442 or A030016.

Cf. A018252, A064113, A065310, A065890, A140119, A173390, A233671, A258025, A258026, A350004, A376602 (zero), A376603 (nonzero), A376651 (positive), A376652 (negative), A376680, A377034, A377035.

Programs

Mathematica

nn=10000;
u=Table[Differences[Select[Range[nn],CompositeQ],k],{k,2,16}];
mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
m=Table[Position[u[[k]],0][[1,1]],{k,mnrm[Union[First/@Position[u,0]]]}]

Extensions

Offset 2 from Michel Marcus, Oct 18 2024

a(17)-a(54) from Alois P. Heinz, Oct 18 2024