cp's OEIS Frontend

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

%I A377037 #15 Oct 18 2024 18:42:46
%S A377037 1,14,2,65,1,83,2,7,1,83,2,424,12,32,11,733,10,940,9,1110,8,1110,7,
%T A377037 1110,6,1110,112,1110,111,1110,110,2192,109,13852,108,13852,107,13852,
%U A377037 106,13852,105,17384,104,17384,103,17384,102,17384,101,27144,552,28012,551
%N A377037 Position of first zero in the n-th differences of the composite numbers (A002808), or 0 if it does not appear.
%H A377037 Alois P. Heinz, <a href="/A377037/b377037.txt">Table of n, a(n) for n = 2..100</a>
%e A377037 The third differences of the composite numbers are:
%e A377037   -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -2, 1, 0, 0, 1, -1, -1, ...
%e A377037 so a(3) = 14.
%t A377037 nn=10000;
%t A377037 u=Table[Differences[Select[Range[nn],CompositeQ],k],{k,2,16}];
%t A377037 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A377037 m=Table[Position[u[[k]],0][[1,1]],{k,mnrm[Union[First/@Position[u,0]]]}]
%Y A377037 The version for prime instead of composite is A376678.
%Y A377037 For noncomposite numbers we have A376855.
%Y A377037 This is the first position of 0 in row n of the array A377033.
%Y A377037 For squarefree instead of composite we have A377042, nonsquarefree A377050.
%Y A377037 For prime-power instead of composite we have A377055.
%Y A377037 Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).
%Y A377037 A000040 lists the primes, differences A001223, second A036263.
%Y A377037 A002808 lists the composite numbers, differences A073783, second A073445.
%Y A377037 A008578 lists the noncomposites, differences A075526.
%Y A377037 A377036 gives first term of the n-th differences of the composite numbers, for primes A007442 or A030016.
%Y A377037 Cf. A018252, A064113, A065310, A065890, A140119, A173390, A233671, A258025, A258026, A350004, A376602 (zero), A376603 (nonzero), A376651 (positive), A376652 (negative), A376680, A377034, A377035.
%K A377037 nonn
%O A377037 2,2
%A A377037 _Gus Wiseman_, Oct 17 2024
%E A377037 Offset 2 from _Michel Marcus_, Oct 18 2024
%E A377037 a(17)-a(54) from _Alois P. Heinz_, Oct 18 2024