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A376855 Position of first 0 in the n-th differences of the noncomposite numbers (A008578), or 0 if it does not appear.

%I A376855 #14 Nov 04 2024 02:58:15
%S A376855 0,0,1,8,70,14,48,59,10,44,3554,101,7020,14083,68098,14527,149678,
%T A376855 2698,481055,979720,631895,29812,25340979,50574255,7510844,210829338,
%U A376855 67248862,224076287,910615648,931510270,452499645,2880203723,396680866,57954439971,77572822441,35394938649
%N A376855 Position of first 0 in the n-th differences of the noncomposite numbers (A008578), or 0 if it does not appear.
%H A376855 Lucas A. Brown, <a href="https://github.com/lucasaugustus/oeis/blob/main/A376855.py">Python program</a>.
%e A376855 The third differences of the noncomposite numbers begin: 1, -1, 2, -4, 4, -4, 4, 0, -6, 8, ... so a(3) = 8.
%t A376855 nn=10000;
%t A376855 u=Table[Differences[Select[Range[nn],#==1||PrimeQ[#]&],k],{k,2,16}];
%t A376855 mnrm[s_]:=If[Min@@s==1,mnrm[DeleteCases[s-1,0]]+1,0];
%t A376855 m=Table[Position[u[[k]],0][[1,1]],{k,mnrm[Union[First/@Position[u,0]]]}]
%Y A376855 For firsts instead of positions of zeros we have A030016, modern A007442.
%Y A376855 These are the first zero-positions in A376682, modern A376678.
%Y A376855 For row-sums instead of zero-positions we have A376683, modern A140119.
%Y A376855 For absolute row-sums we have A376684, modern A376681.
%Y A376855 For composite instead of noncomposite we have A377037.
%Y A376855 For squarefree instead of noncomposite we have A377042, nonsquarefree A377050.
%Y A376855 For prime-power instead of noncomposite we have A377055.
%Y A376855 A000040 lists the modern primes, differences A001223, seconds A036263.
%Y A376855 A008578 lists the noncomposite numbers, first differences A075526.
%Y A376855 Cf. A002808, A064113, A065890, A084758, A173390, A258025, A333214, A333215, A333254, A377033.
%K A376855 nonn
%O A376855 0,4
%A A376855 _Gus Wiseman_, Oct 15 2024
%E A376855 a(16)-a(21) from _Alois P. Heinz_, Oct 18 2024
%E A376855 a(22)-a(35) from _Lucas A. Brown_, Nov 03 2024