A158748 Triangle, read by rows, T(n, k) = (prime(n+1) - prime(k+1))! - (n! - k!).

1, 1, 1, 5, 1, 1, 115, 19, -2, 1, 362857, 40297, 698, 6, 1, 39916681, 3628681, 40202, 606, -94, 1, 1307674367281, 87178290481, 479000882, 3628086, 24, -576, 1, 355687428090961, 20922789882961, 87178286162, 478996566, 35304, -4200, -4318, 1

Offset

0,4

Links

G. C. Greubel, Rows n = 0..50 of the triangle, flattened

Formula

T(n, k) = (prime(n+1) - prime(k+1))! - (n! - k!).

Example

Triangle begins as:
                1;
                1,              1;
                5,              1,           1;
              115,             19,          -2,         1;
           362857,          40297,         698,         6,     1;
         39916681,        3628681,       40202,       606,   -94,     1;
    1307674367281,    87178290481,   479000882,   3628086,    24,  -576,     1;
  355687428090961, 20922789882961, 87178286162, 478996566, 35304, -4200, -4318, 1;
  ...

Mathematica

T[n_, k_]:= (Prime[n+1] - Prime[k+1])! - (n! - k!);
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten

Prog

(Magma) [Factorial(NthPrime(n+1) - NthPrime(k+1)) - Factorial(n) + Factorial(k): k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 01 2021
(Sage) flatten([[factorial(nth_prime(n+1) -nth_prime(k+1)) -factorial(n) +factorial(k) for k in (0..n)] for n in (0..10)]) # G. C. Greubel, Dec 01 2021

Crossrefs

Cf. A000142, A008578.

Sequence in context: A173475 A174919 A156952 * A351241 A273874 A086039

Adjacent sequences: A158745 A158746 A158747 * A158749 A158750 A158751

Keyword

sign,tabl

Author

Roger L. Bagula, Mar 25 2009

Extensions

Edited by G. C. Greubel, Dec 01 2021

Status

approved