cp's OEIS Frontend

A377036 First term of the n-th differences of the composite numbers. Inverse zero-based binomial transform of A002808.

%I A377036 #10 Oct 19 2024 08:32:08
%S A377036 4,2,0,-1,2,-2,0,4,-8,8,0,-16,32,-32,-1,78,-233,687,-2363,8160,-25670,
%T A377036 72352,-184451,430937,-933087,1888690,-3597221,6479696,-11086920,
%U A377036 18096128,-28307626,42644791,-62031001,86466285,-110902034,110907489,-52325,-483682930
%N A377036 First term of the n-th differences of the composite numbers. Inverse zero-based binomial transform of A002808.
%F A377036 The inverse zero-based binomial transform of a sequence (q(0), q(1), ..., q(m)) is the sequence p given by:
%F A377036   p(j) = sum_{k=0..j} (-1)^(j-k) binomial(j,k) q(k)
%t A377036 q=Select[Range[100],CompositeQ];
%t A377036 t=Table[Sum[(-1)^(j-k)*Binomial[j,k]*q[[1+k]],{k,0,j}],{j,0,Length[q]-1}]
%Y A377036 The version for prime instead of composite is A007442.
%Y A377036 For noncomposite numbers we have A030016.
%Y A377036 This is the first column (n=1) of A377033.
%Y A377036 For row-sums we have A377034, absolute version A377035.
%Y A377036 First zero positions are A377037, cf. A376678, A376855, A377042, A377050, A377055.
%Y A377036 For squarefree instead of composite we have A377041, nonsquarefree A377049.
%Y A377036 For prime-power instead of composite we have A377054.
%Y A377036 Other arrays of differences: A095195 (prime), A376682 (noncomposite), A377033 (composite), A377038 (squarefree), A377046 (nonsquarefree), A377051 (prime-power).
%Y A377036 A000040 lists the primes, differences A001223, seconds A036263.
%Y A377036 A002808 lists the composite numbers, differences A073783, seconds A073445.
%Y A377036 A008578 lists the noncomposites, differences A075526.
%Y A377036 Cf: A018252, A065310, A065890, A140119, A173390, A333214, A376602 (zero), A376603 (nonzero), A376651 (positive), A376652 (negative), A376680.
%K A377036 sign
%O A377036 0,1
%A A377036 _Gus Wiseman_, Oct 18 2024