login
A116163
Numbers k such that k concatenated with k+1 gives the product of two numbers which differ by 1.
8
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
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 *)
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