A106575 Perfect squares which are both the sum and the difference of two primes.

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

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

Table of n, a(n) for n=1..47.

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: A000548 A256944 A349062 * 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