OFFSET
0,1
COMMENTS
Primes on the left side of the triangle formed by listing successively the prime numbers in a triangular grid:
2
3 5
7 11 13
17 19 23 29
31 37 41 43 47
53 59 61 67 71 73
The sum of the reciprocals appears to converge.
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
LINKS
Michael De Vlieger, Table of n, a(n) for n = 0..10000
FORMULA
MATHEMATICA
Table[Prime[n (n + 1)/2 + 1], {n, 0, 46}] (* Michael De Vlieger, Oct 28 2015 *)
Prime[#]&/@(Accumulate[Range[0, 50]]+1) (* Harvey P. Dale, Aug 04 2018 *)
PROG
(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); */}
(Magma) [NthPrime(n*(n + 1) div 2+1): n in [0..50]]; // Vincenzo Librandi, Jun 08 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Dec 20 2002
STATUS
approved