A090781 Numbers that can be expressed as the difference of the squares of primes in just one distinct way.

5, 16, 21, 24, 40, 45, 48, 96, 112, 117, 144, 160, 165, 192, 264, 280, 285, 288, 336, 352, 357, 504, 520, 525, 648, 816, 832, 837, 936, 952, 957, 1152, 1344, 1360, 1365, 1368, 1440, 1656, 1672, 1677, 1752, 1824, 1840, 1845, 1872, 1968, 2184, 2200, 2205, 2328

Offset: 1

Author

Ray Chandler, Feb 14 2004

Keywords

• nonn

Examples

			5 = 3^2 - 2^2.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..908

Crossrefs

Cf. A078667, A090788, A090782, A090785.

Programs

Mathematica

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 *)

Python

from sympy import primerange
from collections import Counter
def aupto(limit):
  sqps = [p*p for p in primerange(1, limit//2+1)]
  ways = Counter(b-a for i, a in enumerate(sqps) for b in sqps[i+1:])
  return sorted(k for k in ways if k <= limit and ways[k] == 1)
print(aupto(2328)) # Michael S. Branicky, May 16 2021