A391280 Array read by ascending antidiagonals: T(n,k) is the number of primes p in the range n*(k-1) < p <= n*k.

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

Offset

1,4

Links

Table of n, a(n) for n=1..91.

Formula

T(n,k) = A000720(n * k) - A000720(n * (k-1)).

Example

  \k   1  2  3  4  5  6  7  8  9 10 ...
  n\
   1   0  1  1  0  1  0  1  0  0  0 ...
   2   1  1  1  1  0  1  1  0  1  1 ...
   3   2  1  1  1  1  1  1  1  0  1 ...
   4   2  2  1  1  2  1  0  2  0  1 ...
   5   3  1  2  2  1  1  1  1  2  1 ...
   6   3  2  2  2  1  1  2  2  1  1 ...
   7   4  2  2  1  2  2  2  1  2  1 ...
   8   4  2  3  2  1  3  1  2  2  2 ...
   9   4  3  2  2  3  2  2  2  2  2 ...
  10   4  4  2  2  3  2  2  3  2  1 ...
  ...

Mathematica

T[n_, k_] := PrimePi[n*k] - PrimePi[n(k -1)]; Table[ t[r -c +1, c], {r, 13}, {c, r}] // Flatten

Prog

(PARI) T(n, k) = primepi(n*k) - primepi(n*(k-1)); \\ Michel Marcus, Dec 10 2025

Crossrefs

By rows: (1) A010051, (4) A157865, (9) A155462, (10) A038800, (30) A098592, (100) A038822, (210) A094892, (1000) A038823, (10^4) A038824, (10^5) A038825, (10^6) A038826, (10^7) A038827, (10^8) A038828, (10^9) A038829, (10^10) A038830, (10^11) A038831, (10^12) A038832, (10^13) A080132.

By columns: (1) A000720, (2) A108954, (3) A289493, (4) A289494, (5) A289495, (6) A289496, (7) A289497, (8) A289498, (9) A289499, (10) A289500.

Sequence in context: A336708 A308424 A317489 * A345647 A091950 A014750

Adjacent sequences: A391277 A391278 A391279 * A391281 A391282 A391283

Keyword

easy,nonn,tabl

Author

Robert G. Wilson v, Dec 05 2025

Status

approved