A107787 Golden semiprimes that are not brilliant numbers.

77, 7303, 10033, 15229, 644251, 706609, 836197, 870071, 936791, 1027333, 1177993, 1261807, 1366553, 1433143, 1525441, 1608161, 62259511, 62782091, 63462979, 64441621, 64973261, 65427751, 65599201, 65837659, 66043093, 66834373, 67966247, 70635437, 70882871

Offset: 1

Author

Jason Earls, Jun 14 2005

Keywords

• base
• nonn

Examples

			7303=67*109 is in the sequence because abs(67*phi-109) = 0.59172... < 1 and its prime factors have an unequal number of decimal digits.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A108540, A078972.

Programs

Mathematica

f[p_] := Module[{x = GoldenRatio * p}, p1 = NextPrime[x, -1]; p2 = NextPrime[p1]; q = If[x - p1 < p2 - x, p1, p2]; If[Abs[q - x] < 1, q, 0]]; seq = {}; p = 1; Do[p = NextPrime[p]; q = f[p]; If[q > 0 && IntegerLength[p] != IntegerLength[q], AppendTo[seq, p*q]], {1000}]; seq (* Amiram Eldar, Nov 29 2019 *)

Extensions

More terms from Donovan Johnson, Mar 06 2008