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 A180655 Semiprimes (products of two distinct primes) of the form, next perfect square minus semiprime equals perfect square. 1
 15, 21, 35, 55, 65, 77, 91, 143, 187, 209, 221, 247, 299, 323, 391, 437, 493, 551, 589, 667, 713, 851, 899, 1073, 1147, 1189, 1247, 1271, 1333, 1457, 1517, 1591, 1739, 1763, 1927, 1961, 2021, 2173, 2279, 2419, 2491, 2501, 2537, 2623, 2773, 2867, 3127, 3149 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Table of n, a(n) for n=1..48. Michael M. Ross, Instantly Factor a Semiprime of Any Size! EXAMPLE 3*5=15,16-15=1; 3*7=21;25-21=4->2; 5*13=65,81-65=16->4;... MATHEMATICA f1[n_]:=Last/@FactorInteger[n]=={1, 1}; f2[n_]:=IntegerQ[Sqrt[Ceiling[Sqrt[n]]^2-n]]; lst={}; Do[If[f1[n]&&f2[n], AppendTo[lst, n]], {n, 3*7!}]; lst spQ[n_]:=Module[{nps=Ceiling[Sqrt[n]]^2}, PrimeNu[n]==PrimeOmega[n] == 2 && IntegerQ[Sqrt[nps-n]]]; Select[Range[3200], spQ] (* Harvey P. Dale, Aug 17 2012 *) CROSSREFS Cf. A006881 Sequence in context: A081934 A095147 A081977 * A254365 A335674 A349096 Adjacent sequences: A180652 A180653 A180654 * A180656 A180657 A180658 KEYWORD nonn AUTHOR Vladimir Joseph Stephan Orlovsky, Sep 15 2010 STATUS approved

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Last modified February 25 11:24 EST 2024. Contains 370325 sequences. (Running on oeis4.)