A303502 -id:A303502 - cp's OEIS frontend

A303504 Integers whose digits, together with a single supplementary digit, cannot be reordered to form a base-10 palindrome number.

102, 103, 104, 105, 106, 107, 108, 109, 120, 123, 124, 125, 126, 127, 128, 129, 130, 132, 134, 135, 136, 137, 138, 139, 140, 142, 143, 145, 146, 147, 148, 149, 150, 152, 153, 154, 156, 157, 158, 159, 160, 162, 163, 164, 165, 167, 168, 169, 170, 172, 173, 174, 175, 176, 178, 179, 180, 182, 183

Offset: 1

Eric Angelini and Jean-Marc Falcoz, Apr 25 2018

This is the complement of A303502.

Starts with the 648 terms of A031962. - Georg Fischer, Oct 08 2018

			a(1) = 102 together with a single 0 can form 1002, 1020, 1200, 2001, 2010 and 2100, but none of these are palindromes;
a(1) = 102 together with a single 1 can form 1012, 1021, 1102, 1120, 1201, 1210, 2011, 2101 and 2110, but none of these are palindromes;
etc.

Jean-Marc Falcoz, Table of n, a(n) for n = 1..5184

Cf. A002113 (Palindromes in base 10), A303502 (complement of this sequence).

A373300 Sum of successive integers in a row of length p(n) where p counts integer partitions.

Original entry on oeis.org

1, 5, 15, 45, 105, 264, 555, 1221, 2445, 4935, 9324, 17941, 32522, 59400, 104808, 184569, 315711, 540540, 902335, 1504800, 2462724, 4014513, 6444425, 10316250, 16283707, 25610886, 39841865, 61720659, 94687230, 144731706, 219282679, 330996105, 495901413, 740046425

Offset: 1

Olivier Gérard, May 31 2024

nonn

The length of each row is given by A000041.
As many sequences start like the positive integers, their row sums when disposed in this shape start with the same values.
Here is a sample list by A-number order of the sequences which are sufficiently close to A000027 to have the same row sums for at least 8 terms.
A069782, A088480, A090107, A090108, A090109, A115510, A115511, A130446, A131717, A132086, A153671, A167904, A296879, A296882, A296885, A296888, A296891, A296894, A296897, A296900, A296903, A296906, A303502, A317945, A335280, A361374.

			Let's put the list of integers in a triangle whose rows have length p(n), number of integer partitions of n.
.
    1 |  1
    5 |  2  3
   15 |  4  5  6
   45 |  7  8  9 10 11
  105 | 12 13 14 15 16 17 18
  264 | 19 20 21 22 23 24 25 26 27 28 29
  555 | 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
.
The sequence gives the row sums of this triangle.

Cf. A000027, seen as a triangle with shape A000041.
Cf. A373301, the same principle, but starting from integer zero instead of 1.
Cf. A006003, row sums of the integers but for the linear triangle.

Module[{s = 0},
 Table[s +=
   PartitionsP[n - 1]; (s + PartitionsP[n])*(s + PartitionsP[n] - 1)/2 -
   s*(s - 1)/2, {n, 1, 30}]]

cp's OEIS Frontend

A303504 Integers whose digits, together with a single supplementary digit, cannot be reordered to form a base-10 palindrome number.

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