A351718
Numbers whose binary and maximal Lucas representations are both palindromic.
Original entry on oeis.org
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
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
-
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]] &]]
A352088
Numbers whose binary and minimal tribonacci representations are both palindromic.
Original entry on oeis.org
0, 1, 3, 5, 45, 2193, 7671, 35889, 53835, 74825, 3026205, 31953871, 86582437, 117169915, 128873391, 701373669, 868430067, 15262037703, 45305389845, 104484026691, 614071181169, 14894476590363, 24382189266573, 86808432666553, 869188423288227, 1352557858988953
Offset: 1
The first 5 terms are:
n a(n) A007088(a(n)) A278038(a(n))
-------------------------------------
1 0 0 0
2 1 1 1
3 3 11 11
4 5 101 101
5 45 101101 1000001
-
t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; tribPalQ[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; PalindromeQ[FromDigits @ IntegerDigits[Total[2^(s - 1)], 2]]]; Join[{0}, Select[Range[1, 10^5, 2], PalindromeQ[IntegerDigits[#, 2]] && tribPalQ[#] &]]
A352106
Numbers whose binary and maximal tribonacci representations are both palindromic.
Original entry on oeis.org
0, 1, 3, 5, 7, 27, 51, 325, 2193, 3735, 23709, 35889, 53835, 589833, 1294265, 17291201, 80719769, 1274288105, 23157444917, 23635236877, 230684552043, 1218891196337, 1722894010643, 2544113575977, 93096801594005, 175482093541881, 256924005422487, 372295593308821
Offset: 1
The first 5 terms are:
n a(n) A007088(a(n)) A352103(a(n))
- ---- ------------- -------------
1 0 0 0
2 1 1 1
3 3 11 11
4 5 101 101
5 7 111 111
6 27 11011 11111
7 51 110011 111111
8 325 101000101 111111111
9 2193 100010010001 1001101011001
10 3735 111010010111 1111111111111
-
t[1] = 1; t[2] = 2; t[3] = 4; t[n_] := t[n] = t[n - 1] + t[n - 2] + t[n - 3]; trib[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[t[k] <= m, k++]; k--; AppendTo[s, k]; m -= t[k]; k = 1]; IntegerDigits[Total[2^(s - 1)], 2]]; lazyTribPalQ[n_] := Module[{v = trib[n]}, nv = Length[v]; i = 1; While[i <= nv - 3, If[v[[i ;; i + 3]] == {1, 0, 0, 0}, v[[i ;; i + 3]] = {0, 1, 1, 1}; If[i > 3, i -= 4]]; i++]; i = Position[v, _?(# > 0 &)]; If[i == {}, True, PalindromeQ[FromDigits[v[[i[[1, 1]] ;; -1]]]]]]; Join[{0}, Select[Range[1, 10^5, 2], PalindromeQ[IntegerDigits[#, 2]] && lazyTribPalQ[#] &]]
Showing 1-3 of 3 results.