A084754 Triangle read by rows: row n lists the first n primes greater than n.

2, 3, 5, 5, 7, 11, 5, 7, 11, 13, 7, 11, 13, 17, 19, 7, 11, 13, 17, 19, 23, 11, 13, 17, 19, 23, 29, 31, 11, 13, 17, 19, 23, 29, 31, 37, 11, 13, 17, 19, 23, 29, 31, 37, 41, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59

Offset

1,1

Links

G. C. Greubel, Rows n = 1..100 of the triangle, flattened

Formula

From G. C. Greubel, May 13 2023: (Start)

T(n, k) = prime(PrimePi(n) + k).

T(n, 1) = A151800(n).

T(n, 2) = A101300(n). (End)

Example

Triangle starts:
  2;
  3,  5;
  5,  7, 11;
  5,  7, 11, 13;
  7, 11, 13, 17, 19;
  7, 11, 13, 17, 19, 23;
  ...

Mathematica

Table[Prime[PrimePi[n]+k], {n, 16}, {k, n}]//Flatten (* G. C. Greubel, May 13 2023 *)

Prog

(Magma) [NthPrime(#PrimesUpTo(n) + k): k in [1..n], n in [1..16]]; // G. C. Greubel, May 13 2023
(SageMath)
def A084754(n, k): return nth_prime(prime_pi(n)+k)
flatten([[A084754(n, k) for k in range(1, n+1)] for n in range(1, 17)]) # G. C. Greubel, May 13 2023

Crossrefs

Cf. A000040, A000720, A101300, A151800.

Sequence in context: A332286 A357250 A156898 * A120724 A117530 A238256

Adjacent sequences: A084751 A084752 A084753 * A084755 A084756 A084757

Keyword

nonn,easy,tabl,changed

Author

Amarnath Murthy and Jason Earls, Jul 12 2003

Extensions

Edited by David Wasserman, Jan 05 2005

Status

approved