A011757 a(n) = prime(n^2).
2, 7, 23, 53, 97, 151, 227, 311, 419, 541, 661, 827, 1009, 1193, 1427, 1619, 1879, 2143, 2437, 2741, 3083, 3461, 3803, 4211, 4637, 5051, 5519, 6007, 6481, 6997, 7573, 8161, 8737, 9341, 9931, 10627, 11321, 12049, 12743, 13499, 14327, 15101, 15877, 16747, 17609, 18461
Offset: 1
Examples
a(4) = 53 as the (4^2)th prime is the 16th prime is 53. - _David A. Corneth_, Apr 13 2021
Links
- David A. Corneth, Table of n, a(n) for n = 1..20000 (first 1000 terms from Zak Seidov)
Programs
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Magma
[NthPrime(n^2): n in [1..100] ]; // Vincenzo Librandi, Apr 12 2011
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Mathematica
Prime[Range[40]^2] (* Alonso del Arte, Feb 11 2015 *)
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PARI
a(n)=prime(n^2) \\ Charles R Greathouse IV, Jul 02 2013
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PARI
first(n) = { my(res = vector(n), t = 0); forprime(p = 2, oo, t++; if(ispower(t, 2, &i), print1([i, p]", "); res[i] = p; if(i >= n, return(res)))) } \\ David A. Corneth, Apr 13 2021
Formula
a(n) = n^2 log^2 n + O(n^2 log n log log n). - Charles R Greathouse IV, Mar 11 2014