A072041 a(n) is the smallest number of the form k + reverse(k) for exactly n integers k, or -1 if no such number exists.

1, 0, 22, 33, 44, 55, 66, 77, 88, 99, 1111, -1, 2552, -1, 2662, 3443, 2772, -1, 2882, -1, 2992, 3663, -1, -1, 3773, 5445, -1, 3883, 4664, -1, 3993, -1, 4774, -1, -1, 5665, 4884, -1, -1, -1, 4994, -1, 6666, -1, -1, 5885, -1, -1, 6776, 7667, 5995, -1, -1, -1, 6886

Offset

0,3

Comments

The negative terms are conjectural. Moreover they have a rather low degree of confirmation, since due to the time-consuming computations only numbers from 0 to 65000 have been taken into account. Random tests of larger numbers however seem to indicate, that only selected values of n occur. - In the cognate sequence A071266 two numbers a and b are counted only once, if n = a + b, a = reverse(b), b = reverse(a). Then 33 = 12 + 21 = 30 + 03 has a count of 2 and 44 = 13 + 31 = 22 + 22 = 40 + 04 has a count of 3, so 44 appears in A071266 instead of 33.

Terms are correct for k <= 10^8. - Sean A. Irvine, Aug 27 2024

Links

Table of n, a(n) for n=0..54.

Index entries for sequences related to Reverse and Add!

Example

a(0) = 1, since 1 can in no way be written as k + reverse(k); a(1) = 0, since 0 = k + reverse(k) for k = 0; a(3) = 33, since 33 = k + reverse(k) for k = 12, 21 and 30.

Crossrefs

Cf. A067030, A071266, A072040.

Sequence in context: A157529 A165932 A190588 * A067035 A074054 A067287

Adjacent sequences: A072038 A072039 A072040 * A072042 A072043 A072044

Keyword

base,sign

Author

Klaus Brockhaus, Jun 08 2002

Status

approved