A120724 Irregular triangle T(n, k) = prime(n) + k*(k-1), for n >= 1 and 1 <= k <= 1 + A000720(n), read by rows.

2, 3, 5, 5, 7, 11, 7, 9, 13, 11, 13, 17, 23, 13, 15, 19, 25, 17, 19, 23, 29, 37, 19, 21, 25, 31, 39, 23, 25, 29, 35, 43, 29, 31, 35, 41, 49, 31, 33, 37, 43, 51, 61, 37, 39, 43, 49, 57, 67, 41, 43, 47, 53, 61, 71, 83, 43, 45, 49, 55, 63, 73, 85, 47, 49, 53, 59, 67, 77, 89

Offset

1,1

Links

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

Formula

T(n, k) = prime(k) + 2*Sum_{j=1..n-1} j, for n >= 1 and 1 <= k <= 1 + A000720(n).

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

Example

Irregular triangle begins as:
   2;
   3,  5;
   5,  7, 11;
   7,  9, 13;
  11, 13, 17, 23;
  13, 15, 19, 25;
  17, 19, 23, 29, 37;
  19, 21, 25, 31, 39;
  23, 25, 29, 35, 43;
  29, 31, 35, 41, 49;

Mathematica

T[n_, k_]:= Prime[n] + k*(k-1);
Table[T[n, k], {n, 20}, {k, PrimePi[n]+1}]//Flatten

Prog

(Magma)
A120724:= func< n, k | NthPrime(n) +k*(k-1) >;
[A120724(n, k): k in [1..#PrimesUpTo(n)+1], n in [1..20]]; // G. C. Greubel, Jul 20 2023
(SageMath)
def A120724(n, k): return nth_prime(n) + k*(k-1)
flatten([[A120724(n, k) for k in range(1, prime_pi(n)+2)] for n in range(1, 21)]) # G. C. Greubel, Jul 20 2023

Crossrefs

Cf. A000040, A000720.

Sequence in context: A357250 A156898 A084754 * A117530 A238256 A239277

Adjacent sequences: A120721 A120722 A120723 * A120725 A120726 A120727

Keyword

nonn,tabf,easy

Author

Roger L. Bagula, Aug 18 2006

Extensions

Edited by G. C. Greubel, Jul 20 2023

Status

approved