This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Select[Prime[Range[200]],PrimeQ[(#^2-5)/4]&]
Select[Prime[Range[200]],PrimeQ[(#^2-13)/12]&]
7 is prime and appears in the sequence because (7^3 - 4)/3 = 113 which is a prime. 31 is prime and appears in the sequence because (31^3 - 4)/3 = 9929 which is a prime.
KD:= proc() local a,b;a:=ithprime(n); b:=(a^3-4)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);
Select[Prime[Range[500]], PrimeQ[(#^3 - 4)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 - 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)
s=[]; forprime(p=2, 4000, if((p^3-4)%3==0 && isprime((p^3-4)/3), s=concat(s, p))); s \\ Colin Barker, Apr 16 2014
[p: p in PrimesUpTo(10^7) | IsPrime((p^2+5) div 6) and IsPrime((p^4+5) div 6) and IsPrime((p^6+5) div 6)]; // Vincenzo Librandi, Jan 21 2015
Select[Prime[Range[10^7]], PrimeQ[(#^2 + 5) / 6] &&PrimeQ[(#^4 + 5) / 6] &&PrimeQ[(#^6 + 5) / 6] &] (* Vincenzo Librandi, Jan 21 2015 *) Select[Prime[Range[3*10^5]],AllTrue[(#^{2,4,6}+5)/6,PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 10 2016 *)
a(1) = 19 is prime: (19^3 + 6)/ 5 = 1373 which is also prime. a(2) = 59 is prime: (59^3 + 6)/ 5 = 41077 which is also prime.
KD:= proc() local a,b; a:=ithprime(n); b:=(a^3+6)/5; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..5000);
Select[Prime[Range[5000]], PrimeQ[(#^3 + 6)/5] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 6)/5], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (*b-file*)
s=[]; forprime(p=2, 20000, if((p^3+6)%5==0 && isprime((p^3+6)/5), s=concat(s, p))); s \\ Colin Barker, Apr 21 2014
5 is prime and appears in the sequence because (5^3 + 4)/3 = 43 which is a prime. 23 is prime and appears in the sequence because (23^3 + 4)/3 = 4057 which is a prime.
KD:= proc() local a,b;a:=ithprime(n); b:=(a^3+4)/3; if b=floor(b) and isprime(b) then RETURN (a); fi; end: seq(KD(), n=1..1000);
Select[Prime[Range[500]], PrimeQ[(#^3 + 4)/3] &]
n = 0; Do[If[PrimeQ[(Prime[k]^3 + 4)/3], n = n + 1; Print[n, " ", Prime[k]]], {k, 1, 200000}] (* b-file *)
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