A352319 Numbers whose minimal (or greedy) Pell representation (A317204) is palindromic.

0, 1, 3, 6, 8, 13, 20, 30, 35, 40, 44, 49, 71, 88, 102, 119, 170, 182, 194, 204, 216, 238, 242, 254, 266, 276, 288, 409, 450, 484, 525, 559, 580, 621, 655, 696, 986, 1015, 1044, 1068, 1097, 1150, 1160, 1189, 1218, 1242, 1271, 1334, 1363, 1392, 1396, 1425, 1454

Offset

1,3

Comments

A052937(n) = A000129(n+1)+1 is a term for n>0, since its minimal Pell representation is 10...01 with n-1 0's between two 1's.

A048739 is a subsequence since these are repunit numbers in the minimal Pell representation.

A001109 is a subsequence. The minimal Pell representation of A001109(n), for n>1, is 1010...01, with n-1 0's interleaved with n 1's.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

The first 10 terms are:
   n  a(n)  A317204(a(n))
  --  ----  -------------
   1     0              0
   2     1              1
   3     3             11
   4     6            101
   5     8            111
   6    13           1001
   7    20           1111
   8    30          10001
   9    35          10101
  10    40          10201

Mathematica

pell[1] = 1; pell[2] = 2; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; q[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[pell[k] <= m, k++]; k--; AppendTo[s, k]; m -= pell[k]; k = 1]; PalindromeQ[IntegerDigits[Total[3^(s - 1)], 3]]]; Select[Range[0, 1500], q]

Crossrefs

Cf. A000129, A317204.

Subsequences: A001109, A048739, A052937 \ {2}.

Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087.

Sequence in context: A346597 A108161 A263349 * A297211 A365314 A345318

Adjacent sequences: A352316 A352317 A352318 * A352320 A352321 A352322

Keyword

nonn,base

Author

Amiram Eldar, Mar 12 2022

Status

approved