A376855 Position of first 0 in the n-th differences of the noncomposite numbers (A008578), or 0 if it does not appear.

0, 0, 1, 8, 70, 14, 48, 59, 10, 44, 3554, 101, 7020, 14083, 68098, 14527, 149678, 2698, 481055, 979720, 631895, 29812, 25340979, 50574255, 7510844, 210829338, 67248862, 224076287, 910615648, 931510270, 452499645, 2880203723, 396680866, 57954439971, 77572822441, 35394938649

Offset: 0

Author

Gus Wiseman, Oct 15 2024

Keywords

• nonn

Examples

			The third differences of the noncomposite numbers begin: 1, -1, 2, -4, 4, -4, 4, 0, -6, 8, ... so a(3) = 8.
		

Links

• Lucas A. Brown, Python program.

Crossrefs

For firsts instead of positions of zeros we have A030016, modern A007442.

These are the first zero-positions in A376682, modern A376678.

For row-sums instead of zero-positions we have A376683, modern A140119.

For absolute row-sums we have A376684, modern A376681.

For composite instead of noncomposite we have A377037.

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

For prime-power instead of noncomposite we have A377055.

A000040 lists the modern primes, differences A001223, seconds A036263.

A008578 lists the noncomposite numbers, first differences A075526.

Cf. A002808, A064113, A065890, A084758, A173390, A258025, A333214, A333215, A333254, A377033.

Programs

Mathematica

nn=10000;
u=Table[Differences[Select[Range[nn],#==1||PrimeQ[#]&],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

a(16)-a(21) from Alois P. Heinz, Oct 18 2024

a(22)-a(35) from Lucas A. Brown, Nov 03 2024