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