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

1,3

Links

Table of n, a(n) for n=1..28.

Example

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

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[#] &]]

Crossrefs

Intersection of A006995 and A352105.

Cf. A007088, A352103.

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

Sequence in context: A126669 A126668 A083518 * A061944 A288924 A093574

Adjacent sequences: A352103 A352104 A352105 * A352107 A352108 A352109

Keyword

nonn,base

Author

Amiram Eldar, Mar 05 2022

Status

approved