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A090781
Numbers that can be expressed as the difference of the squares of primes in just one distinct way.
27
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
1,1
EXAMPLE
5 = 3^2 - 2^2.
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
Ray Chandler, Feb 14 2004
STATUS
approved