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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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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.

Original entry on oeis.org

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

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Author

Klaus Brockhaus, Jun 08 2002

Keywords

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

Examples

			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.

Links

Crossrefs

Cf. A067030, A071266, A072040.

A071265 Numbers which can be written in exactly two different ways as k + R(k) where R(k) is k reversed (A004086).

Original entry on oeis.org

22, 33, 165, 176, 202, 222, 242, 262, 282, 302, 303, 322, 323, 342, 343, 362, 363, 382, 383, 403, 423, 443, 463, 483, 1515, 1535, 1555, 1575, 1595, 1615, 1616, 1635, 1636, 1655, 1656, 1675, 1676, 1695, 1696, 1716, 1736, 1756, 1776, 1796, 2002, 2871, 3003
Offset: 1

Views

Author

Amarnath Murthy, Jun 01 2002

Keywords

Comments

The sums are unordered, so for example 12 + 21 is not counted as distinct from 21 + 12. - Sean A. Irvine, Jul 06 2024

Examples

			22 = 11 + 11 = 20 + 02, 202 =101 + 101 = 200 + 002.

Links

Crossrefs

Cf. A071264, A071266, A067030, A067032, A067033, A067034.

Extensions

More terms from Vladeta Jovovic and Klaus Brockhaus, Jun 03 2002
Offset corrected by Sean A. Irvine, Jul 06 2024
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