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A143541
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Triangle read by rows, T(n,k) = 1 if both n and k are prime, 0 otherwise; 1 <= k <= n.
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3
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0, 0, 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 0, 1
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OFFSET
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1,1
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COMMENTS
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Row sums = the prime count, A049084: (0, 1, 2, 0, 3, 0, 4, 0, 0, 0, 5, ...).
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LINKS
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FORMULA
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Triangle read by rows, T(n,k) = 1 if n & k are prime, 0 otherwise.
The n-th row = n zeros if n is a nonprime; first n terms of A010051 (the characteristic function of primes) if n is prime.
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EXAMPLE
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First few rows of the triangle are:
0;
0, 1;
0, 1, 1;
0, 0, 0, 0;
0, 1, 1, 0, 1;
0, 0, 0, 0, 0, 0;
0, 1, 1, 0, 1, 0, 1;
...
Row 5 = first 5 terms of A010051: (0, 1, 1, 0, 1).
T(5,3) = 1 since (5,3) are prime; but T(5,4) = 0 since 4 is a nonprime.
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MAPLE
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T:=(n, k)->`if`(isprime(n) and isprime(k), 1, 0): seq(seq(T(n, k), k=1..n), n=1..12); # Muniru A Asiru, Oct 28 2018
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MATHEMATICA
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nn = 11; Flatten[Table[Table[If[And[PrimeQ[n], PrimeQ[k]], 1, 0], {k, 1, n}], {n, 1, nn}]] (* Mats Granvik, Oct 28 2018 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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