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

%I A011756 #44 Feb 16 2025 08:32:32
%S A011756 2,5,13,29,47,73,107,151,197,257,317,397,467,571,659,769,883,1019,
%T A011756 1151,1291,1453,1607,1783,1987,2153,2371,2593,2791,3037,3307,3541,
%U A011756 3797,4073,4357,4657,4973,5303,5641,5939,6301,6679,7019,7477
%N A011756 a(n) = prime(n*(n+1)/2).
%C A011756 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
%H A011756 Reinhard Zumkeller, <a href="/A011756/b011756.txt">Table of n, a(n) for n = 1..1000</a>
%H A011756 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TriangularNumber.html">Triangular Number</a>.
%F A011756 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
%F A011756 a(n) = A000040(A000217(n)). - _David James Sycamore_, Sep 03 2024
%p A011756 seq(ithprime(n*(n+1)/2),n=1..50); # _Muniru A Asiru_, Jul 22 2018
%t A011756 Prime[#]&/@Accumulate[Range[50]] (* _Harvey P. Dale_, Mar 23 2015 *)
%o A011756 (Magma) [NthPrime(n*(n+1) div 2): n in [1..100] ]; // _Vincenzo Librandi_, Apr 11 2011
%o A011756 (Haskell)
%o A011756 a011756 n = a011756_list !! (n-1)
%o A011756 a011756_list = map a000040 $ tail a000217_list
%o A011756 -- _Reinhard Zumkeller_, Sep 23 2011
%o A011756 (PARI) a(n) = prime(n*(n+1)/2); \\ _Michel Marcus_, Jul 22 2018
%Y A011756 Primes in leading diagonal of triangle in A078721.
%Y A011756 Cf. A000040, A000217, A034953.
%Y A011756 Cf. A195678.
%Y A011756 Cf. A000720.
%K A011756 nonn
%O A011756 1,1
%A A011756 _Jeff Burch_