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A078721 a(n) = prime(n*(n+1)/2 + 1). 10
2, 3, 7, 17, 31, 53, 79, 109, 157, 199, 263, 331, 401, 479, 577, 661, 773, 887, 1021, 1153, 1297, 1459, 1609, 1787, 1993, 2161, 2377, 2609, 2797, 3041, 3313, 3547, 3803, 4079, 4363, 4663, 4987, 5309, 5647, 5953, 6311, 6689, 7027, 7481, 7841, 8263, 8689 (list; graph; refs; listen; history; text; internal format)
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

a(n) = A000040(A000124(n)). - Altug Alkan, Oct 28 2015

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

Cf. A000040, A011756, A078722, A078723, etc.

Sequence in context: A268539 A083822 A030086 * A077007 A158498 A267601

Adjacent sequences:  A078718 A078719 A078720 * A078722 A078723 A078724

KEYWORD

nonn,easy

AUTHOR

Cino Hilliard, Dec 20 2002

STATUS

approved

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Last modified September 17 04:49 EDT 2019. Contains 327119 sequences. (Running on oeis4.)