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

Author

Amarnath Murthy and Jason Earls, Jul 12 2003

Keywords

• nonn
• easy
• tabl

Examples

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

Links

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

Crossrefs

Cf. A000040, A000720, A101300, A151800.

Programs

Magma

[NthPrime(#PrimesUpTo(n) + k): k in [1..n], n in [1..16]]; // G. C. Greubel, May 13 2023

Mathematica

Table[Prime[PrimePi[n]+k], {n,16}, {k,n}]//Flatten (* 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

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)

Extensions

Edited by David Wasserman, Jan 05 2005