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A143538 Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n.

%I A143538 #12 Sep 21 2021 11:28:50
%S A143538 0,0,1,0,1,1,0,1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,1,1,0,1,0,
%T A143538 1,0,0,1,1,0,1,0,1,0,0,0,1,1,0,1,0,1,0,0,0,0,1,1,0,1,0,1,0,0,0,1
%N A143538 Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n.
%C A143538 Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n. A000012 * (A010051 * 0^(n-k)). A010051 * 0^(n-k) = an infinite lower triangular matrix with A010051 (the characteristic function of the primes) as the main diagonal and the rest zeros. The multiplier A000012 takes partial sums of column terms.
%H A143538 G. C. Greubel, <a href="/A143538/b143538.txt">Table of n, a(n) for the first 100 rows, flattened</a>
%F A143538 a(n) = A010051(A002260(n)). - _Wesley Ivan Hurt_, Sep 20 2021
%e A143538 First few rows of the triangle =
%e A143538 0;
%e A143538 0, 1;
%e A143538 0, 1, 1;
%e A143538 0, 1, 1, 0;
%e A143538 0, 1, 1, 0, 1;
%e A143538 0, 1, 1, 0, 1, 0;
%e A143538 0, 1, 1, 0, 1, 0, 1;
%e A143538 ...
%t A143538 Table[If[PrimeQ[k], 1, 0], {n, 1, 20}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Sep 17 2017 *)
%o A143538 (PARI) for(n=1,10, for(k=1,n, print1(if(isprime(k),1,0), ", "))) \\ _G. C. Greubel_, Sep 17 2017
%Y A143538 Cf. A000720 (row sums), A002260, A010051.
%K A143538 nonn,tabl
%O A143538 1,1
%A A143538 _Gary W. Adamson_, Aug 23 2008