A123387 Number of triangular numbers <= n-th prime.

2, 3, 3, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 17, 18, 18, 18, 19, 19, 19, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22, 22, 23, 23, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 26, 26, 26, 26, 27, 27, 27, 27

Offset: 1

Author

Giovanni Teofilatto, Nov 10 2006

Keywords

• easy
• nonn

Comments

Variant of A057062. - R. J. Mathar, Dec 13 2008

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000040, A000217, A002024, A003056.

Programs

Mathematica

f[n_] := Round[Sqrt[2n + 2]]; Table[f[Prime[n]], {n, 90}] (* Ray Chandler, Nov 13 2006 *)

Python

from math import isqrt
from sympy import prime
def A123387(n): return isqrt(prime(n)+1<<3)+1>>1 # Chai Wah Wu, Oct 18 2022

Formula

a(n) = A003056(A000040(n)) + 1 = A002024(A000040(n) + 1).

a(n) ~ sqrt(2n log n). - Charles R Greathouse IV, Oct 18 2022

Extensions

Extended by Ray Chandler, Nov 13 2006