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Amiram Eldar, <a href="/A352319/b352319.txt">Table of n, a(n) for n = 1..10000</a>

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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.

allocated for Amiram EldarNumbers 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

1,3

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.

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

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]

Cf. A000129, A317204.

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

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

allocated

nonn,base

Amiram Eldar, Mar 12 2022

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allocated for Amiram Eldar

allocated

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