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URL: https://oeis.org/A106564

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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
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
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
KEYWORD
easy,nonn
AUTHOR
Alexandre Wajnberg, May 09 2005
EXTENSIONS
Extended by Ray Chandler, May 12 2005
STATUS
approved