A377055 Position of first appearance of zero in the n-th differences of the prime-powers (A246655), or 0 if it does not appear.

0, 0, 1, 1, 4, 48, 61, 83, 29, 57, 290, 121, 7115, 14207, 68320, 14652, 149979, 122704, 481540, 980376, 632441, 29973, 25343678, 50577935, 7512418, 210836403, 67253056, 224083553, 910629561, 931524323, 452509699, 2880227533, 396690327, 57954538325, 77572935454, 35395016473

Offset: 0

Author

Gus Wiseman, Oct 22 2024

Keywords

• nonn

Examples

			The fourth differences of A246655 begin: 1, -3, 3, 0, -2, 2, ... so a(4) = 4.
		

Links

• Lucas A. Brown, Python program.

Crossrefs

The version for primes is A376678, noncomposites A376855, composites A377037.

For squarefree numbers we have A377042, nonsquarefree A377050.

These are the positions of first zeros in each row of A377051.

For antidiagonal-sums we have A377052, absolute A377053.

For leaders we have A377054, for primes A007442 or A030016.

A000040 lists the primes, differences A001223, seconds A036263.

A000961 lists the powers of primes, differences A057820.

A008578 lists the noncomposites, differences A075526.

A023893 and A023894 count integer partitions into prime-powers, factorizations A000688.

A246655 lists the prime-powers, differences A057820 (except first term).

Cf. A025475, A053707, A093555, A174965, A175804, A361102, A376340, A376596, A377056.

Programs

Mathematica

nn=10000;
u=Table[Differences[Select[Range[nn],PrimePowerQ],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(12)-a(27) from Pontus von Brömssen, Oct 22 2024

a(28)-a(30) from Chai Wah Wu, Oct 23 2024

a(31)-a(35) from Lucas A. Brown, Nov 03 2024