A110589 Primes p such that 2*q+3 = p^2, where q is prime.
3, 5, 7, 11, 13, 19, 23, 29, 31, 37, 41, 47, 67, 73, 79, 97, 101, 103, 109, 151, 157, 197, 211, 227, 233, 239, 257, 263, 293, 307, 331, 337, 349, 353, 359, 367, 389, 397, 409, 443, 449, 463, 487, 491, 509, 521, 547, 569, 571, 587, 613, 619, 653, 661, 673, 727
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
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Magma
[p: p in PrimesUpTo(1000) | IsPrime((p^2-3) div 2)]; // Vincenzo Librandi, Mar 19 2015
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Maple
ispower := proc(n,b) andmap(proc(w) evalb(w[2] mod b = 0) end, ifactors(n)[2]) end: a:=2: SQRTP||a:=[]; for z from 1 to 1 do for n from 1 to 10000 do p:=ithprime(n); m:=a*p+a+1; if ispower(m,2) and isprime(sqrt(m)) then SQRTP||a:=[op(SQRTP||a),sqrt(m)] fi od; od; SQRTP||a;
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Mathematica
fQ[n_] := PrimeQ[(n^2 - 3)/2]; Select[ Prime@ Range@129, fQ@# &] (* Robert G. Wilson v, Jun 19 2006 *) Select[Table[Sqrt[2 Prime[n] + 3], {n, 1, 30000}], PrimeQ] (* Vincenzo Librandi, Mar 19 2015 *)
Extensions
More terms from Robert G. Wilson v, Jun 19 2006