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

1,2

Comments

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A116154, A115426, A116170, A116294.

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

Sequence in context: A258672 A326571 A201254 * A092823 A152031 A302181

Adjacent sequences: A116160 A116161 A116162 * A116164 A116165 A116166

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

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

More terms from Giovanni Resta, Jul 08 2018

Status

approved