A261912 -id:A261912 - 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.

A261913 The palindromic order of n (defined in Comments).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2

Offset: 0

N. J. A. Sloane, Sep 10 2015

Order 1: palindromes (A002113);
Order 2: not order 1 but is the sum of two palindromes (A261907);
Order 3: not order 1 or 2, but n - previous_palindrome(n) (i.e., n - A261914(n)) gives a number of order 2 (A261910);
Order 4: not order 1, 2, or 3, but subtracting previous_palindrome(previous_palindrome(n)) gives a number of order 2 (A261911);
Order 5: not orders 1, 2, 3, or 4 (A261912).

N. J. A. Sloane, Table of n, a(n) for n = 0..20000

Cf. A002113, A261423, A261907, A261910, A261911, A261912, A261914.

Closely related to A261675. See also A088601.

a(n) = A088601(n). - R. J. Mathar, Feb 14 2023

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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A261913 The palindromic order of n (defined in Comments).

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