A116193 Numbers k such that k concatenated with k+5 gives the product of two numbers which differ by 5.

11, 45, 18281, 32769, 56891, 180689, 330539, 959481, 1850201, 3247409, 4940219, 2425563239, 2575561739, 6003563495, 7245212645, 7770160145, 4983798265289, 5049762270381, 5534298528989, 5603798594169, 21894082450101

Offset

1,1

Comments

Also numbers k such that k concatenated with k+9 gives the product of two numbers which differ by 3. For proof that this is the same sequence compare A116133.

Also numbers k such that k concatenated with k-9 gives the product of two numbers which differ by 9.

If k+5 has d digits, the concatenation is k//k+5 = 10^d*k+k+5 = m*(m+5), therefore k//k-1 = 10^d*k+k-1 = (m-1)*(m+6), so there is a large overlap with A116152. - R. J. Mathar, May 22 2026

Links

Table of n, a(n) for n=1..21.

Example

7770160145//7770160136 = 8814851183 * 8814851192, where // denotes concatenation.

Crossrefs

Cf. A116205, A116187, A116349.

Cf. A116179, A115430, A116194, A116200, A116324.

Cf. A116099, A116109, A116231.

Sequence in context: A231438 A322560 A110114 * A282095 A063158 A396288

Adjacent sequences: A116190 A116191 A116192 * A116194 A116195 A116196

Keyword

nonn,base

Author

Giovanni Resta, Feb 06 2006

Extensions

Edited by N. J. A. Sloane, Apr 12 2007

Status

approved