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A088239 Triangle read by rows: T(n,k) is the number of primes not less than n-k and not greater than n+k, 0<=k<n. 0

%I #10 Sep 18 2021 04:20:35

%S 0,1,2,1,2,3,0,2,3,4,1,1,3,4,4,0,2,2,3,4,5,1,1,2,2,4,5,6,0,1,1,3,3,5,

%T 6,6,0,0,2,2,4,4,5,6,7,0,1,1,3,3,4,4,6,7,8,1,1,2,2,3,3,5,5,7,8,8,0,2,

%U 2,2,2,4,4,6,6,7,8,9,1,1,2,2,3,3,5,5,6,6,8,9,9,0,1,1,3,3,4,4,5,5,7,7,8,9,9

%N Triangle read by rows: T(n,k) is the number of primes not less than n-k and not greater than n+k, 0<=k<n.

%F T(n,0) = A010051(n); T(n,n-1) = A000720(2*n-1).

%e Triangle begins:

%e 0;

%e 1, 2;

%e 1, 2, 3;

%e 0, 2, 3, 4;

%e 1, 1, 3, 4, 4;

%e 0, 2, 2, 3, 4, 5;

%e ...

%t T[n_, k_] := PrimePi[n+k] - PrimePi[n-k-1];

%t Table[T[n, k], {n, 1, 14}, {k, 0, n-1}] // Flatten (* _Jean-François Alcover_, Sep 18 2021 *)

%Y Cf. A000720, A010051.

%K nonn,tabl

%O 1,3

%A _Reinhard Zumkeller_, Nov 03 2003

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)