A352106 Numbers whose binary and maximal tribonacci representations are both palindromic.

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

Author

Amiram Eldar, Mar 05 2022

Keywords

• nonn
• base

Examples

			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
		

Crossrefs

Intersection of A006995 and A352105.

Cf. A007088, A352103.

Similar sequences: A095309, A331193, A331894, A351713, A351718, A352088.

Programs

Mathematica

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[#] &]]