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A078721
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a(n) = prime(n*(n+1)/2 + 1).
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11
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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
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OFFSET
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0,1
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COMMENTS
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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
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LINKS
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FORMULA
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MATHEMATICA
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Prime[#]&/@(Accumulate[Range[0, 50]]+1) (* Harvey P. Dale, Aug 04 2018 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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