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Numbers that can be expressed as the difference of the squares of primes in just one distinct way.
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%I #13 May 16 2021 07:58:12

%S 5,16,21,24,40,45,48,96,112,117,144,160,165,192,264,280,285,288,336,

%T 352,357,504,520,525,648,816,832,837,936,952,957,1152,1344,1360,1365,

%U 1368,1440,1656,1672,1677,1752,1824,1840,1845,1872,1968,2184,2200,2205,2328

%N Numbers that can be expressed as the difference of the squares of primes in just one distinct way.

%H T. D. Noe, <a href="/A090781/b090781.txt">Table of n, a(n) for n=1..908</a>

%e 5 = 3^2 - 2^2.

%t With[{nn=100},Take[Sort[Transpose[Select[Tally[Last[#]-First[#]&/@ Subsets[ Prime[Range[nn]]^2,{2}]],Last[#]==1&]][[1]]],nn]] (* _Harvey P. Dale_, Apr 05 2014 *)

%o (Python)

%o from sympy import primerange

%o from collections import Counter

%o def aupto(limit):

%o sqps = [p*p for p in primerange(1, limit//2+1)]

%o ways = Counter(b-a for i, a in enumerate(sqps) for b in sqps[i+1:])

%o return sorted(k for k in ways if k <= limit and ways[k] == 1)

%o print(aupto(2328)) # _Michael S. Branicky_, May 16 2021

%Y Cf. A078667, A090788, A090782, A090785.

%K nonn

%O 1,1

%A _Ray Chandler_, Feb 14 2004