|
|
A078721
|
|
a(n) = prime(n*(n+1)/2 + 1).
|
|
11
|
|
|
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
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
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,changed
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|