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A376683 Antidiagonal-sums of the array A376682(n,k) = n-th term of the k-th differences of the noncomposite numbers (A008578).

%I A376683 #8 Oct 17 2024 08:25:10
%S A376683 1,3,4,9,6,27,-20,109,-182,471,-868,1737,-2872,4345,-4700,1133,14060,
%T A376683 -55275,150462,-346093,717040,-1369351,2432872,-4002905,5964846,
%U A376683 -7524917,6123130,4900199,-40900410,134309057,-348584552,798958881,-1678213106,3277459119
%N A376683 Antidiagonal-sums of the array A376682(n,k) = n-th term of the k-th differences of the noncomposite numbers (A008578).
%e A376683 The fourth anti-diagonal of A376682 is: (7, 2, 0, -1, -2), so a(4) = 6.
%t A376683 nn=12;
%t A376683 t=Table[Take[Differences[NestList[NestWhile[#+1&,#+1,!PrimeQ[#]&]&,1,2*nn],k],nn],{k,0,nn}];
%t A376683 Total/@Table[t[[j,i-j+1]],{i,nn},{j,i}]
%Y A376683 The modern version (for A000040 instead of A008578) is A140119.
%Y A376683 The absolute version is A376681.
%Y A376683 Antidiagonal-sums of A376682 (modern version A095195).
%Y A376683 For composite instead of noncomposite we have A377033.
%Y A376683 For squarefree instead of noncomposite we have A377038, nonsquarefree A377046.
%Y A376683 A000040 lists the modern primes, differences A001223, second A036263.
%Y A376683 A008578 lists the noncomposites, first differences A075526.
%Y A376683 Cf. A007442, A030016, A064113, A065890, A002808, A173390, A233671, A333214, A333254, A376678, A376684, A376855.
%K A376683 sign
%O A376683 0,2
%A A376683 _Gus Wiseman_, Oct 15 2024