cp's OEIS Frontend

A377050 Position of first appearance of zero in the n-th differences of the nonsquarefree numbers, or 0 if it does not appear.

%I A377050 #11 Oct 26 2024 10:48:37
%S A377050 0,0,5,11,4,129,10,89,16,161,72,77325,71,4870,70,253,75,737923,166,
%T A377050 1648316,165,8753803,164,208366710,163,99489971,162,49493333,161
%N A377050 Position of first appearance of zero in the n-th differences of the nonsquarefree numbers, or 0 if it does not appear.
%C A377050 If a(29) is not 0, then it is > 10^12. - _Lucas A. Brown_, Oct 25 2024
%H A377050 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A377050.py">Python program</a>.
%e A377050 The fourth differences of A013929 begin: -6, -2, 5, 0, -7, 9, -6, 6, -7, ... so a(4) = 4.
%t A377050 nn=10000;
%t A377050 u=Table[Differences[Select[Range[nn],!SquareFreeQ[#]&],k],{k,2,16}];
%t A377050 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A377050 m=Table[Position[u[[k]],0][[1,1]],{k,mnrm[Union[First/@Position[u,0]]]}]
%Y A377050 The version for primes is A376678, noncomposites A376855, composites A377037.
%Y A377050 For squarefree instead of nonsquarefree numbers we have A377042.
%Y A377050 For antidiagonal-sums we have A377047, absolute A377048.
%Y A377050 For leading column we have A377049.
%Y A377050 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377050 A005117 lists the squarefree numbers.
%Y A377050 A013929 lists the nonsquarefree numbers, differences A078147, seconds A376593.
%Y A377050 A073576 counts integer partitions into squarefree numbers, factorizations A050320.
%Y A377050 Cf. A000961, A007674, A053797, A053806, A061398, A072284, A084758, A112925, A120992, A376311, A376591, A377051.
%K A377050 nonn,more
%O A377050 0,3
%A A377050 _Gus Wiseman_, Oct 19 2024
%E A377050 a(17)-a(28) from _Lucas A. Brown_, Oct 25 2024