A351717 - OEIS

A351717

Numbers whose maximal (or lazy) Lucas representation (A130311) is palindromic.

0, 2, 3, 5, 6, 10, 12, 14, 17, 20, 28, 30, 34, 36, 42, 46, 56, 61, 75, 77, 85, 92, 94, 101, 107, 115, 122, 128, 150, 166, 176, 198, 200, 211, 219, 233, 244, 246, 260, 271, 277, 288, 296, 310, 321, 345, 360, 396, 405, 441, 469, 484, 520, 522, 544, 562, 570, 588

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OFFSET

1,2

COMMENTS

A001610(n) = Lucas(n+1) - 1 is a term for all n, since A001610(0) = 0 has the representation 0 and the representation of Lucas(n+1) - 1 is n 1's for n > 0.

LINKS

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

Index entries for sequences related to palindromes.

EXAMPLE

The first 10 terms are:

n a(n) A130311(a(n))

----------------------

1 0 0

2 2 1

3 3 11

4 5 101

5 6 111

6 10 1111

7 12 10101

8 14 11011

9 17 11111

10 20 101101

MATHEMATICA

lazy = Select[IntegerDigits[Range[6000], 2], SequenceCount[#, {0, 0}] == 0 &]; t = Total[# * Reverse @ LucasL[Range[0, Length[#] - 1]]] & /@ lazy; s = FromDigits /@ lazy[[TakeWhile[Flatten[FirstPosition[t, #] & /@ Range[Max[t]]], NumberQ]]]; Join[{0}, Position[s, _?PalindromeQ] // Flatten]

CROSSREFS

Cf. A000032, A001610, A130311.

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

Sequence in context: A099350 A337218 A306296 * A191173 A240026 A213212

Adjacent sequences: A351714 A351715 A351716 * A351718 A351719 A351720

KEYWORD

nonn,base

AUTHOR

Amiram Eldar, Feb 17 2022

STATUS

approved