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Squares of the form 2*p+3 that are squares of primes.
1

%I #6 Aug 06 2013 09:07:44

%S 9,25,49,121,169,361,529,841,961,1369,1681,2209,4489,5329,6241,9409,

%T 10201,10609,11881,22801,24649,38809,44521,51529,54289,57121,66049,

%U 69169,85849,94249,109561,113569,121801,124609

%N Squares of the form 2*p+3 that are squares of primes.

%H Charles R Greathouse IV, <a href="/A110588/b110588.txt">Table of n, a(n) for n = 1..10000</a>

%p ispower := proc(n,b) andmap(proc(w) evalb(w[2] mod b = 0) end, ifactors(n)[2]) end: a:=2: PW||a:=[]; for z from 1 to 1 do for n from 1 to 1000 do p:=ithprime(n); m:=a*p+a+1; if ispower(m,2) and isprime(sqrt(m)) then PW||a:=[op(PW||a),m] fi od; od; PW||a;

%o (PARI) isok(n) = issquare(n) && isprime(sqrtint(n)) && (type(p=(n-3)/2) == "t_INT") && isprime(p) \\ _Michel Marcus_, Aug 06 2013

%o (PARI) v=List();forprime(p=2,1e4,if(isprime(p^2\2-1),listput(v,p^2))); Vec(v) \\ _Charles R Greathouse IV_, Aug 06 2013

%Y Cf. A098828, A109358.

%K nonn

%O 1,1

%A _Walter Kehowski_, Sep 13 2005

%E More terms from _Michel Marcus_, Aug 06 2013