A180655 Semiprimes (products of two distinct primes) of the form, next perfect square minus semiprime equals perfect square.

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

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