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A176451 Number of primes between two consecutive nonprimes in A037143.

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%I A176451 #14 Sep 07 2024 08:54:10
%S A176451 2,1,1,0,2,0,2,0,1,0,2,0,0,1,0,2,1,0,1,0,0,2,0,1,2,0,1,1,0,0,1,0,0,0,
%T A176451 3,2,1,0,0,0,0,0,1,1,0,2,0,0,0,0,2,1,0,0,1,1,1,0,2,0,0,2,2,0,0,0,0,0,
%U A176451 1,0,0,0,0,0,0,1,3,0,2,0,1,0,1,0,1,0,2,1,2,0,0,1,0,0,0,0,0,0,1,2,1,0,0,0,0
%N A176451 Number of primes between two consecutive nonprimes in A037143.
%C A176451 2 together with the number of primes between successive semiprimes.
%H A176451 Amiram Eldar, <a href="/A176451/b176451.txt">Table of n, a(n) for n = 1..10000</a>
%F A176451 a(n) = A088700(n-1) for n >= 2.
%e A176451 a(1) = 2 because A037143(1) = 1 (nonprime) < A037143(2) = 2 (prime) < A037143(3) = 3 (prime) < A037143(4) = 4 (nonprime).
%t A176451 Join[{2}, -1 + Differences[Position[Select[PrimeOmega[Range[400]], # < 3 &], 2] // Flatten]] (* _Amiram Eldar_, Sep 07 2024 *)
%Y A176451 Cf. A001358, A037143, A088700.
%K A176451 nonn,easy
%O A176451 1,1
%A A176451 _Juri-Stepan Gerasimov_, Apr 18 2010