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A351718
Numbers whose binary and maximal Lucas representations are both palindromic.
3
0, 3, 5, 17, 85, 107, 219, 1161, 1365, 1619, 2047, 4097, 6141, 19801, 25027, 68961, 91213, 134337, 1540157, 1804859, 11877549, 37696497, 44092437, 142710801, 548269377, 3387848595, 4073444175, 8226780335, 31029923047, 64662095631, 67947722943, 126590440407, 2145176968607
OFFSET
1,2
EXAMPLE
The first 10 terms are:
n a(n) A007088(a(n)) A130311(a(n))
----------------------------------------
1 0 0 0
2 3 11 11
3 5 101 101
4 17 10001 11111
5 85 1010101 101101101
6 107 1101011 111010111
7 219 11011011 10110101101
8 1161 10010001001 11011111111011
9 1365 10101010101 101010101010101
10 1619 11001010011 101111010111101
MATHEMATICA
lazy = Select[IntegerDigits[Range[10^6], 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}, Select[Position[s, _?PalindromeQ] // Flatten, PalindromeQ[IntegerDigits[#, 2]] &]]
CROSSREFS
Intersection of A006995 and A351717.
Sequence in context: A102295 A365518 A227335 * A281627 A102846 A100003
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Feb 17 2022
STATUS
approved