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%I #18 Sep 08 2022 08:45:18
%S 4,9,16,36,64,81,100,144,196,225,256,324,400,441,484,576,676,784,900,
%T 1024,1089,1156,1296,1444,1600,1764,1936,2116,2304,2500,2704,2916,
%U 3136,3364,3600,3844,4096,4356,4624,4900,5184,5476,5776,6084,6400,6724,7056
%N Perfect squares which are both the sum and the difference of two primes.
%C Equals A106548 with 0's removed.
%C Appears to contain all even squares.
%C By well-known conjectures, every even integer > 2 is both the sum and the difference of two primes; this would be a special case. - _Franklin T. Adams-Watters_, Sep 13 2015
%e 2^2 = 4 is in the sequence because it is the sum of two primes (2+2) and the difference of two primes (7-3). 10^2 = 100 is in the sequence because it is the sum and the difference of two primes: 97+3 (or 89+11) and 103-3. 11^2 = 121 is not in the sequence because it is neither the sum nor the difference of two primes. 13^2 = 169 is the sum of two primes (167+2), but it doesn't figure here since it is not the difference of two primes.
%o (Magma) [ s: n in [1..85] | exists(t){ k: k in [1..s] | s-k gt 0 and IsPrime(k) and IsPrime(s-k) } and exists(u){ k: k in [1..s] | IsPrime(k) and IsPrime(s+k) } where s is n^2 ]; /* _Klaus Brockhaus_, Nov 17 2010 */
%Y Cf. A106544-A106548, A106562-A106564, A106571, A106573, A106574, A106577.
%K easy,nonn
%O 1,1
%A _Alexandre Wajnberg_, May 09 2005
%E Extended by _Ray Chandler_, May 12 2005
%E Edited by _Klaus Brockhaus_, Nov 17 2010
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