A261913 -id:A261913 - cp's OEIS frontend

A261910 Numbers n which are neither palindromes nor the sum of two palindromes, with property that subtracting the largest palindrome < n from n gives a number which is the sum of two palindromes.

21, 32, 43, 54, 65, 76, 87, 98, 201, 1031, 1041, 1042, 1051, 1052, 1053, 1061, 1062, 1063, 1064, 1071, 1072, 1073, 1074, 1075, 1081, 1082, 1083, 1084, 1085, 1086, 1091, 1092, 1093, 1094, 1095, 1096, 1097, 1101, 1103, 1104, 1105, 1106, 1107, 1108, 1109, 1123, 1124, 1125, 1126, 1127, 1128, 1129, 1134, 1135, 1136, 1137, 1138, 1139, 1145, 1146, 1147, 1148, 1149, 1153

Offset: 1

N. J. A. Sloane, Sep 10 2015

These are the numbers with palindromic order 3 (see A261913).

More than the usual number of terms are shown in order to clarify the difference between this sequence and A035137.

N. J. A. Sloane, Table of n, a(n) for n = 1..9937

A subset of A035137.

Cf. A002113, A261675, A261911, A261912, A261913.

A261911 Numbers n which are neither palindromes nor the sum of two palindromes, with property that the largest palindrome which when subtracted from n yields the sum of two palindromes is not the palindromic floor of n (A261423(n)), but rather the next palindrome below that.

Original entry on oeis.org

1099, 1143, 1154, 1165, 1176, 1187, 1198, 1209, 1264, 1275, 1286, 1297, 1308, 1319, 1385, 1396, 1407, 1418, 1429, 1517, 1528, 1539, 1638, 1649, 1759, 10099, 10155, 10199, 10299, 10366, 10399, 10499, 10577, 10599, 10699, 10799, 11809, 12819, 13829, 14839

Offset: 1

N. J. A. Sloane, Sep 10 2015

These are the numbers with palindromic order 4 (see A261913).

N. J. A. Sloane, Table of n, a(n) for n = 1..51

Cf. A002113, A261423, A261910, A261912, A261913.

A261912 Numbers with palindromic order 5.

Original entry on oeis.org

101073, 101082, 101100, 101155, 101199, 102192, 102299, 103275, 103293, 103366, 103399, 103502, 104332, 104342, 104352, 104362, 104372, 104382, 104392, 104499, 104602, 105432, 105442, 105452, 105462, 105472, 105482, 105492, 105493, 105544, 105577, 105599, 105702

Offset: 1

N. J. A. Sloane, Sep 10 2015

See A261913 for definition.
In the Friedman Problem of the Month page, there is a statement by John Hoffman which, if I have interpreted it correctly, asserts that this sequence has only a finite number of terms. However, Chai Wah Wu has extended the sequence out to 10^8, finding 481384 terms, the last one being a(481384) = 99998180. This sequence does not appear to be finite.
The first terms of this sequence are just beyond A109326(5). It can be expected that at least beyond A109326(6) = 1000101024 there will be examples where N-prevpal(N) and N-prevpal(prevpal(N)) are both of order 5; these numbers could be termed to be of order 6, and so on. - M. F. Hasler, Sep 13 2015

Chai Wah Wu, Table of n, a(n) for n = 1..2278
Erich Friedman, Problem of the Month (June 1999)
M. F. Hasler, Sum of palindromes, OEIS wiki, Sep 10 2015
Chai Wah Wu, Table of n, a(n) for n = 1..481384 (zipped file)

Cf. A002113, A261907, A261910, A261911, A261913, A262528.

More terms from Chai Wah Wu, Sep 11 2015 and Sep 12 2015

cp's OEIS Frontend

A261910 Numbers n which are neither palindromes nor the sum of two palindromes, with property that subtracting the largest palindrome < n from n gives a number which is the sum of two palindromes.

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A261911 Numbers n which are neither palindromes nor the sum of two palindromes, with property that the largest palindrome which when subtracted from n yields the sum of two palindromes is not the palindromic floor of n (A261423(n)), but rather the next palindrome below that.

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A261912 Numbers with palindromic order 5.

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