cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A090781 #13 May 16 2021 07:58:12
%S A090781 5,16,21,24,40,45,48,96,112,117,144,160,165,192,264,280,285,288,336,
%T A090781 352,357,504,520,525,648,816,832,837,936,952,957,1152,1344,1360,1365,
%U A090781 1368,1440,1656,1672,1677,1752,1824,1840,1845,1872,1968,2184,2200,2205,2328
%N A090781 Numbers that can be expressed as the difference of the squares of primes in just one distinct way.
%H A090781 T. D. Noe, <a href="/A090781/b090781.txt">Table of n, a(n) for n=1..908</a>
%e A090781 5 = 3^2 - 2^2.
%t A090781 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 A090781 (Python)
%o A090781 from sympy import primerange
%o A090781 from collections import Counter
%o A090781 def aupto(limit):
%o A090781   sqps = [p*p for p in primerange(1, limit//2+1)]
%o A090781   ways = Counter(b-a for i, a in enumerate(sqps) for b in sqps[i+1:])
%o A090781   return sorted(k for k in ways if k <= limit and ways[k] == 1)
%o A090781 print(aupto(2328)) # _Michael S. Branicky_, May 16 2021
%Y A090781 Cf. A078667, A090788, A090782, A090785.
%K A090781 nonn
%O A090781 1,1
%A A090781 _Ray Chandler_, Feb 14 2004