A200525 Zeisel numbers with p(0)=4.

385, 2585, 7315, 8911, 27001, 39905, 48391, 87283, 192211, 196285, 319705, 410089, 425585, 441091, 624605, 679855, 1310185, 1899163, 2460439, 2586971, 2777041, 6654005, 7042411, 7501261, 8291459, 9516637, 10484585, 11141671, 12527281, 13015891, 13788319

Offset: 1

Author

Karsten Meyer, Nov 18 2011

Keywords

• nonn

Comments

Pick any integers A and B and consider the linear recurrence relation given by p(0) = 4, p(i + 1) = A*p(i) + B. If for some n > 2, p(1), p(2), ..., p(n) are distinct primes, then the product of these primes is called a Zeisel number.

Examples

			a=2, b=-3 => p(1) = (4*2)+(-3) = 5; p(2) = (5*2)+(-3) = (7); p(3) = (7*2)+(-3) = 11 => 5*7*11 = 385.
a=2, b=5 => p(1) = (4*2)+5 = 13; p(2) = (13*2)+5 = 31; p(3) = (31*2)+5 = 67 => 13*31*67 = 27001.
		

Links

• Eric Weisstein's World of Mathematics, Zeisel Number.
• Wikipedia, Zeisel number

Crossrefs

Cf. A051015.

Programs

Rexx

n0=4
do m=1 to 53
  a=2*m
  do b=(1-(4*a)) to 999
    n1=(n0*a)+b
    n2=(n1*a)+b
    n3=(n2*a)+b
    z=n1*n2*n3
    say n0 a b
    lineout("zeisel_4.txt",z||" = "||n1||"*"||n2||"*"||n3||"      "||a||" "||b||" n0="||n0)
    end
  end