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Triangle read by rows, T(n,k) = 1 if k is prime, 0 otherwise; 1 <= k <= n.
3

%I #12 Sep 21 2021 11:28:50

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

%C 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 G. C. Greubel, <a href="/A143538/b143538.txt">Table of n, a(n) for the first 100 rows, flattened</a>

%F a(n) = A010051(A002260(n)). - _Wesley Ivan Hurt_, Sep 20 2021

%e First few rows of the triangle =

%e 0;

%e 0, 1;

%e 0, 1, 1;

%e 0, 1, 1, 0;

%e 0, 1, 1, 0, 1;

%e 0, 1, 1, 0, 1, 0;

%e 0, 1, 1, 0, 1, 0, 1;

%e ...

%t Table[If[PrimeQ[k], 1, 0], {n, 1, 20}, {k, 1, n}] // Flatten (* _G. C. Greubel_, Sep 17 2017 *)

%o (PARI) for(n=1,10, for(k=1,n, print1(if(isprime(k),1,0), ", "))) \\ _G. C. Greubel_, Sep 17 2017

%Y Cf. A000720 (row sums), A002260, A010051.

%K nonn,tabl

%O 1,1

%A _Gary W. Adamson_, Aug 23 2008