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Amiram Eldar, <a href="/A351712/b351712.txt">Table of n, a(n) for n = 1..10000</a>

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allocatedNumbers whose minimal (or forgreedy) Lucas Amiramrepresentation (A130310) is Eldarpalindromic.

0, 2, 6, 9, 13, 20, 24, 31, 49, 56, 64, 78, 100, 125, 136, 150, 158, 169, 201, 237, 252, 324, 342, 364, 378, 396, 404, 422, 444, 523, 581, 606, 650, 708, 845, 874, 910, 932, 961, 975, 1004, 1040, 1048, 1077, 1113, 1135, 1164, 1366, 1460, 1500, 1572, 1666, 1692, 1786

1,2

A000211(n) = Lucas(n) + 2 is a term for all n > 2, since the representation of Lucas(n) + 2 is 10...01 with n-1 0's between the two 1's.

<a href="/index/Pac#palindromes">Index entries for sequences related to palindromes</a>.

The first 10 terms are:

n a(n) A130310(a(n))

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1 0 0

2 2 1

3 6 1001

4 9 10001

5 13 100001

6 20 1000001

7 24 1001001

8 31 10000001

9 49 100000001

10 56 100010001

lucasPalQ[n_] := Module[{s = {}, m = n, k = 1}, While[m > 0, If[m == 1, k = 1; AppendTo[s, k]; m = 0, If[m == 2, k = 0; AppendTo[s, k]; m = 0, While[LucasL[k] <= m, k++]; k--; AppendTo[s, k]; m -= LucasL[k]; k = 1]]]; PalindromeQ[IntegerDigits[Total[2^s], 2]]]; Select[Range[0, 2000], lucasPalQ]

Cf. A000032, A000211, A130310.

Subsequence of A054770.

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

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nonn,base

Amiram Eldar, Feb 17 2022

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allocated for Amiram Eldar

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