A116163 Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 1.

1, 5, 61, 65479, 84289, 106609, 225649, 275599, 453589, 1869505, 2272555, 2738291, 3221951, 1667833021, 2475062749, 2525062249, 3500010739, 9032526511, 9225507211, 1753016898055, 1860598847399, 3233666953849, 3379207972471, 5632076031055, 5823639407489

Offset: 1

Author

Giovanni Resta, Feb 06 2006

Keywords

• nonn
• base

Comments

Also numbers k such that k concatenated with k-1 gives the product of two numbers which differ by 3.

Examples

			1 is a member since 12 = 3*4; also 10 = 2*5.
5 is a member since 56 = 7*8; also 54 = 6*9.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A116154, A115426, A116170, A116294.

Cf. A116143, A102567, A116112, A116130, A116280.

Programs

Mathematica

Union @@ ((y /. List@ ToRules@ Reduce[x (x+1) == 10^# y +y+1 && x>0 && 10^(#-1) <= y+1 < 10^#, {x,y}, Integers]) & /@ Range[13] /. y->{}) (* Giovanni Resta, Jul 08 2018 *)

Extensions

Edited by N. J. A. Sloane, Apr 15 2007, Jun 27 2009

More terms from Giovanni Resta, Jul 08 2018