A011756 a(n) = prime(n*(n+1)/2).

2, 5, 13, 29, 47, 73, 107, 151, 197, 257, 317, 397, 467, 571, 659, 769, 883, 1019, 1151, 1291, 1453, 1607, 1783, 1987, 2153, 2371, 2593, 2791, 3037, 3307, 3541, 3797, 4073, 4357, 4657, 4973, 5303, 5641, 5939, 6301, 6679, 7019, 7477

Offset: 1

Author

Jeff Burch

Keywords

• nonn

Comments

There are n distinct successive primes p (not appearing in the sequence) such that a(n) < p < a(n+1). - David James Sycamore, Jul 22 2018

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Triangular Number.

Crossrefs

Primes in leading diagonal of triangle in A078721.

Cf. A000040, A000217, A034953.

Cf. A195678.

Cf. A000720.

Programs

Haskell

a011756 n = a011756_list !! (n-1)
a011756_list = map a000040 $ tail a000217_list
-- Reinhard Zumkeller, Sep 23 2011

Magma

[NthPrime(n*(n+1) div 2): n in [1..100] ]; // Vincenzo Librandi, Apr 11 2011

Maple

seq(ithprime(n*(n+1)/2),n=1..50); # Muniru A Asiru, Jul 22 2018

Mathematica

Prime[#]&/@Accumulate[Range[50]] (* Harvey P. Dale, Mar 23 2015 *)

PARI

a(n) = prime(n*(n+1)/2); \\ Michel Marcus, Jul 22 2018

Formula

a(n) is asymptotic to (n*(n+1)/2) * log(n*(n+1)/2) = (n*(n+1)/2) * (log(n)+log(n+1)-log(2)) ~ (n^2 + n)*(2 log n)/2 ~ (n^2 + n)*(log n). - Jonathan Vos Post, Mar 12 2006

a(n) = A000040(A000217(n)). - David James Sycamore, Sep 03 2024