A266279 -id:A266279 - cp's OEIS frontend

A082810 Palindromes in which every digit occurs with equal frequency.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 222, 333, 444, 555, 666, 777, 888, 999, 1001, 1111, 1221, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2002, 2112, 2222, 2332, 2442, 2552, 2662, 2772, 2882, 2992, 3003, 3113, 3223, 3333, 3443

Offset: 1

Amarnath Murthy, Apr 21 2003

A superset of A010785. Can someone calculate the index of a term k having d digits? There are terms like 1, 2, 3, 4, 5, 6, 7, 8, 9, 1331, 2442, 3553, ... which have the property that a(31) = 1331, a(42) = 2442, a(53) = 3553 etc. Are there infinitely many such terms?

The additional terms with that property, up to a(100000), are: a(64) = 4664, a(75) = 5775, a(86) = 6886, a(97) = 7997, a(749) = 947749, a(4978) = 87944978, a(46581) = 185640046581. - Georg Fischer, Jan 12 2022

			132231 is a term.

Georg Fischer, Table of n, a(n) for n = 1..10000

Cf. A002113, A010785, A266279.

A373301 Sum of successive nonnegative integers in a row of length p(n) where p counts integer partitions.

Original entry on oeis.org

0, 3, 12, 40, 98, 253, 540, 1199, 2415, 4893, 9268, 17864, 32421, 59265, 104632, 184338, 315414, 540155, 901845, 1504173, 2461932, 4013511, 6443170, 10314675, 16281749, 25608450, 39838855, 61716941, 94682665, 144726102

Offset: 1

Olivier Gérard, May 31 2024

nonn

The length of each row is given by A000041.
As many sequences start like the nonnegative 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 A001477 to have the same row sums for at least 8 terms: A089867, A089868, A089869, A089870, A118760, A123719, A130696, A136602, A254109, A258069, A258070, A258071, A266279, A272813, A273885, A273886, A273887, A273888.

			Illustration of the first few terms
.
0   | 0
3   | 1,  2
12  | 3,  4,  5
40  | 6,  7,  8,  9,  10
98  | 11, 12, 13, 14, 15, 16, 17
253 | 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28
540 | 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43
.

Cf. A373300, original version, with positive integers A000027.
Cf. A001477, the nonnegative integers.
Cf. A027480, the sequence of row sums for a regular triangle.

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

cp's OEIS Frontend

A082810 Palindromes in which every digit occurs with equal frequency.

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