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%I #25 Sep 08 2022 08:45:08
%S 2,3,7,17,31,53,79,109,157,199,263,331,401,479,577,661,773,887,1021,
%T 1153,1297,1459,1609,1787,1993,2161,2377,2609,2797,3041,3313,3547,
%U 3803,4079,4363,4663,4987,5309,5647,5953,6311,6689,7027,7481,7841,8263,8689
%N a(n) = prime(n*(n+1)/2 + 1).
%C Primes on the left side of the triangle formed by listing successively the prime numbers in a triangular grid:
%C 2
%C 3 5
%C 7 11 13
%C 17 19 23 29
%C 31 37 41 43 47
%C 53 59 61 67 71 73
%C The sum of the reciprocals appears to converge.
%C As the terms grow faster than the triangular numbers and the sum of inverse numbers converges, the sum of inverses indeed converges. - _Joerg Arndt_, Oct 28 2015
%H Michael De Vlieger, <a href="/A078721/b078721.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = A000040(A000124(n)). - _Altug Alkan_, Oct 28 2015
%t Table[Prime[n (n + 1)/2 + 1], {n, 0, 46}] (* _Michael De Vlieger_, Oct 28 2015 *)
%t Prime[#]&/@(Accumulate[Range[0,50]]+1) (* _Harvey P. Dale_, Aug 04 2018 *)
%o (PARI) triprimes(n) = { sr = 0; for(j=0,n, x = j*(j+1)/2+1; z = prime(x); sr+=1.0/z; print1(z, ", "); ); print(); /* print(sr); */}
%o (Magma) [NthPrime(n*(n + 1) div 2+1): n in [0..50]]; // _Vincenzo Librandi_, Jun 08 2016
%Y Cf. A000040, A011756, A078722, A078723, etc.
%K nonn,easy
%O 0,1
%A _Cino Hilliard_, Dec 20 2002
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