A068062 -id:A068062 - cp's OEIS frontend

A068064 a(n) = number of integers k such that palindrome A068062(n) = k + reverse(k).

1, 1, 1, 1, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 9, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 1, 10, 3, 4, 5, 6, 7, 8, 9, 10, 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 4, 8, 12, 16, 20, 24

Offset: 1

Klaus Brockhaus, Feb 16 2002

The number of representations of a palindrome as a + b, where b = reverse(a); if a = reverse(b) and a is different from b, then a + b and b + a count as different representations.

			a(9) = 4, since A068062(9) = 44 and for k = 13, 22, 31, 40 we have 44 = k + reverse(k).
a(16) = 9, since A068062(16) = 121 and for k = 29, 38, 47, 56, 65, 74, 83, 92, 110 we have 121 = k + reverse(k).

Cf. A002113, A067030, A067032, A068062.

Offset corrected by Sean A. Irvine, Jan 23 2024

A068061 Palindromic numbers j that are not of the form k + reverse(k) for any k.

Original entry on oeis.org

1, 3, 5, 7, 9, 111, 131, 151, 171, 191, 212, 232, 252, 272, 292, 313, 333, 353, 373, 393, 414, 434, 454, 474, 494, 515, 535, 555, 575, 595, 616, 636, 656, 676, 696, 717, 737, 757, 777, 797, 818, 838, 858, 878, 898, 919, 939, 959, 979, 999, 10101, 10301, 10501

Offset: 1

Klaus Brockhaus, Feb 15 2002

Intersection of A002113 and A067031. Every palindrome with an even number of digits is of the form k + reverse(k), for example 123321 = 123000 + 000321, so the sequence has no terms with an even number of digits.
It seems that the terms follow a strict pattern: x1x', x3x', x5x', x7x', x9x', y1y', y3y', y5y', y7y', y9y' and so on. x' is reverse(x). Apart from the first 5 terms in the sequence, the surrounding terms (x and y) simply iterate over the positive integers. - Dmitry Kamenetsky, Mar 10 2017
Every palindrome with an odd number of digits is of the form k + reverse(k) if the central digit is even, for example 1234321 = 1232000 + 0002321, so no term with an odd number of digits has an even central digit. - A.H.M. Smeets, Feb 01 2019

			9 belongs to this sequence, since there is no k such that k + reverse(k) = 9 (cf. A067031).

Michel Marcus, Table of n, a(n) for n = 1..500

Cf. A002113, A067031, A068062.

isok(n) = {if (Pol(d=digits(n)) == Polrev(d), for (k=1, n-1, if (k + fromdigits(Vecrev(digits(k))) == n, return (0));); 1;);} \\ Michel Marcus, Mar 12 2017

A068065 Palindromes n for which there is a unique k such that n = k + reverse(k).

Original entry on oeis.org

0, 2, 4, 6, 8, 11, 101, 141, 161, 181, 1001, 10001, 10201, 10401, 10601, 10801, 100001, 1000001, 1002001, 1004001, 1006001, 1008001, 10000001, 100000001, 100020001, 100040001, 100060001, 100080001, 1000000001, 10000000001

Offset: 1

Klaus Brockhaus, Feb 16 2002

Subsequence of A068062; A068062(k) is in this sequence if and only if A068064(k) = 1. At first sight, 121 seems to be missing, but in fact 121 does not belong here (cf. example in A068064).

			10601 is in the sequence, since 10601 = 10300 + 00301 and for no other k we have 10601 = k + reverse(k).

Cf. A002113, A067030, A067032, A068062, A068064.

cp's OEIS Frontend

A068064 a(n) = number of integers k such that palindrome A068062(n) = k + reverse(k).

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A068061 Palindromic numbers j that are not of the form k + reverse(k) for any k.

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A068065 Palindromes n for which there is a unique k such that n = k + reverse(k).

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