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 A106575 Perfect squares which are both the sum and the difference of two primes. 13
 4, 9, 16, 36, 64, 81, 100, 144, 196, 225, 256, 324, 400, 441, 484, 576, 676, 784, 900, 1024, 1089, 1156, 1296, 1444, 1600, 1764, 1936, 2116, 2304, 2500, 2704, 2916, 3136, 3364, 3600, 3844, 4096, 4356, 4624, 4900, 5184, 5476, 5776, 6084, 6400, 6724, 7056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equals A106548 with 0's removed. Appears to contain all even squares. 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 LINKS EXAMPLE 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. PROG (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 */ CROSSREFS Cf. A106544-A106548, A106562-A106564, A106571, A106573, A106574, A106577. Sequence in context: A068952 A000548 A256944 * A025620 A117218 A226076 Adjacent sequences:  A106572 A106573 A106574 * A106576 A106577 A106578 KEYWORD easy,nonn AUTHOR Alexandre Wajnberg, May 09 2005 EXTENSIONS Extended by Ray Chandler, May 12 2005 Edited by Klaus Brockhaus, Nov 17 2010 STATUS approved

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Last modified October 21 16:25 EDT 2019. Contains 328302 sequences. (Running on oeis4.)