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A106564 Perfect squares which are not the difference of two primes.

%I A106564 #27 Sep 08 2022 08:45:18
%S A106564 25,49,121,169,289,361,529,625,729,841,961,1225,1369,1681,1849,2209,
%T A106564 2401,2601,2809,3025,3481,3721,3969,4225,4489,4761,5041,5329,5625,
%U A106564 5929,6241,6889,7225,7569,7921,8281,8649,9025,9409,10201,10609,11449,11881
%N A106564 Perfect squares which are not the difference of two primes.
%C A106564 Squares in A269345; see also the Mathematica code. - _Waldemar Puszkarz_, Feb 27 2016
%C A106564 It is conjectured (see A020483) that every even number is a difference of primes, and this is known to be true for even numbers < 10^11.  If so,this sequence consists of the odd squares n such that n+2 is composite. - _Robert Israel_, Feb 28 2016
%H A106564 Robert Israel, <a href="/A106564/b106564.txt">Table of n, a(n) for n = 1..10000</a>
%F A106564 n^2 - A106546 with 0's removed.
%e A106564 a(2)=49 because it is the second perfect square which is impossible to obtain subtracting a prime from another one.
%e A106564 64 is not in the sequence because 64=67-3 (difference of two primes).
%p A106564 remove(t -> isprime(t+2), [seq(i^2, i=1..1000, 2)]); # _Robert Israel_, Feb 28 2016
%t A106564 With[{lst=Union[(#[[2]]-#[[1]])&/@Subsets[Prime[Range[2000]], {2}]]}, Select[Range[140]^2, !MemberQ[lst,#]&]] (* _Harvey P. Dale_, Jan 04 2011 *)
%t A106564 Select[Range[1,174,2]^2, !PrimeQ[#+2]&]
%t A106564 Select[Select[Range[30000], OddQ[#]&& !PrimeQ[#]&& !PrimeQ[#+2]&], IntegerQ[Sqrt[#]]&] (* _Waldemar Puszkarz_, Feb 27 2016 *)
%o A106564 (PARI) for(n=1, 174, n%2==1&&!isprime(n^2+2)&&print1(n^2, ", ")) \\ _Waldemar Puszkarz_, Feb 27 2016
%o A106564 (Magma) [n^2: n in [1..150]| not IsPrime(n^2+2) and n mod 2 eq 1]; // _Vincenzo Librandi_, Feb 28 2016
%Y A106564 Cf. A020483, A106544-A106548, A106562-A106563, A106571, A106573-A106575, A106577.
%K A106564 easy,nonn
%O A106564 1,1
%A A106564 _Alexandre Wajnberg_, May 09 2005
%E A106564 Extended by _Ray Chandler_, May 12 2005