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A376681 Row sums of the absolute value of the array A095195(n, k) = n-th term of the k-th differences of the prime numbers (A000040).

%I A376681 #14 Oct 18 2024 02:53:20
%S A376681 2,4,8,10,22,36,72,134,266,500,874,1418,2044,2736,4626,15176,41460,
%T A376681 95286,196368,372808,660134,1092790,1682198,2384724,3147706,4526812,
%U A376681 11037090,36046768,93563398,214796426,452129242,885186658,1619323680,2763448574,4368014812
%N A376681 Row sums of the absolute value of the array A095195(n, k) = n-th term of the k-th differences of the prime numbers (A000040).
%e A376681 The fourth row of A095195 is: (7, 2, 0, -1), so a(4) = 10.
%t A376681 nn=15;
%t A376681 t=Table[Take[Differences[NestList[NestWhile[#+1&, #+1,!PrimeQ[#]&]&,2,2*nn],k],nn],{k,0,nn}]
%t A376681 Total/@Abs/@Table[t[[j,i-j+1]],{i,nn},{j,i}]
%Y A376681 For firsts instead of row-sums we have A007442 (modern version of A030016).
%Y A376681 This is the absolute version of A140119.
%Y A376681 If 1 is considered prime (A008578) we get A376684, absolute version of A376683.
%Y A376681 For first zero-positions we have A376678 (modern version of A376855).
%Y A376681 For composite instead of prime we have A377035.
%Y A376681 For squarefree instead of prime we have A377040, nonsquarefree A377048.
%Y A376681 A000040 lists the modern primes, differences A001223, seconds A036263.
%Y A376681 A008578 lists the noncomposites, differences A075526, seconds A036263 with 0 prepended.
%Y A376681 Cf. A064113, A065890, A084758, A173390, A233671, A258025, A333214, A333254, A376602, A376651, A376652, A377033.
%K A376681 nonn
%O A376681 1,1
%A A376681 _Gus Wiseman_, Oct 15 2024
%E A376681 More terms from _Pontus von Brömssen_, Oct 17 2024