A181721 The smallest number k such that the product k*n contains digit-reverse(n) as a substring.

1, 1, 1, 1, 1, 1, 1, 1, 1, 101, 1, 18, 24, 101, 34, 101, 42, 45, 48, 51, 6, 1, 14, 101, 21, 24, 27, 65, 32, 101, 23, 72, 1, 101, 101, 101, 29, 22, 24, 26, 28, 22, 8, 1, 12, 14, 42, 8, 6, 21, 3, 49, 67, 27, 1, 101, 75, 32, 5, 51

Offset: 1

Author

Claudio Meller, Nov 17 2010

Keywords

• nonn
• base

Comments

Here, the digit-reverse operation is defined to preserve trailing zeros: for n=10, digit-reverse(n) = 01 which is a substring of 101*10=1010, so a(10)=101. - R. J. Mathar, Nov 17 2010

Crossrefs

Cf. A181720.

Programs

Maple

A181721 := proc(n) nrev := ListTools[Reverse](convert(n,base,10)) ; for k from 1 do  dgskn := convert(k*n,base,10) ; if verify(nrev,dgskn,sublist) then  return k; end if; end do: end proc:
seq(A181721(n),n=1..80) ; # R. J. Mathar, Nov 17 2010

Formula

a(n) = A181720(n)/n. - Michel Marcus, Aug 12 2015