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 A106564 Perfect squares which are not the difference of two primes. 15
 25, 49, 121, 169, 289, 361, 529, 625, 729, 841, 961, 1225, 1369, 1681, 1849, 2209, 2401, 2601, 2809, 3025, 3481, 3721, 3969, 4225, 4489, 4761, 5041, 5329, 5625, 5929, 6241, 6889, 7225, 7569, 7921, 8281, 8649, 9025, 9409, 10201, 10609, 11449, 11881 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Squares in A269345; see also the Mathematica code. - Waldemar Puszkarz, Feb 27 2016 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 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA n^2 - A106546 with 0's removed. EXAMPLE a(2)=49 because it is the second perfect square which is impossible to obtain subtracting a prime from another one. 64 is not in the sequence because 64=67-3 (difference of two primes). MAPLE remove(t -> isprime(t+2), [seq(i^2, i=1..1000, 2)]); # Robert Israel, Feb 28 2016 MATHEMATICA With[{lst=Union[(#[[2]]-#[[1]])&/@Subsets[Prime[Range[2000]], {2}]]}, Select[Range[140]^2, !MemberQ[lst, #]&]] (* Harvey P. Dale, Jan 04 2011 *) Select[Range[1, 174, 2]^2, !PrimeQ[#+2]&] Select[Select[Range[30000], OddQ[#]&& !PrimeQ[#]&& !PrimeQ[#+2]&], IntegerQ[Sqrt[#]]&] (* Waldemar Puszkarz, Feb 27 2016 *) PROG (PARI) for(n=1, 174, n%2==1&&!isprime(n^2+2)&&print1(n^2, ", ")) \\ Waldemar Puszkarz, Feb 27 2016 (MAGMA) [n^2: n in [1..150]| not IsPrime(n^2+2) and n mod 2 eq 1]; // Vincenzo Librandi, Feb 28 2016 CROSSREFS Cf. A020483, A106544-A106548, A106562-A106563, A106571, A106573-A106575, A106577. Sequence in context: A110484 A110013 A109861 * A104777 A289829 A131706 Adjacent sequences:  A106561 A106562 A106563 * A106565 A106566 A106567 KEYWORD easy,nonn AUTHOR Alexandre Wajnberg, May 09 2005 EXTENSIONS Extended by Ray Chandler, May 12 2005 STATUS approved

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Last modified August 17 05:27 EDT 2018. Contains 313810 sequences. (Running on oeis4.)