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

1,1

Links

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

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

Cf. A078667, A090788, A090782, A090785.

Sequence in context: A204920 A168469 A124865 * A191264 A077469 A022140

Adjacent sequences: A090778 A090779 A090780 * A090782 A090783 A090784

Keyword

nonn

Author

Ray Chandler, Feb 14 2004

Status

approved