A354885 Numbers that are palindromes in both ternary and balanced ternary representations.

0, 1, 4, 10, 13, 16, 28, 40, 52, 82, 91, 112, 121, 160, 244, 280, 328, 364, 484, 730, 757, 820, 847, 976, 1003, 1066, 1093, 1312, 1456, 2188, 2296, 2440, 2548, 2920, 3028, 3172, 3280, 3904, 4372, 6562, 6643, 6832, 6913, 7300, 7381, 7570, 7651, 8752, 8833, 9022

Offset

1,3

Links

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

Example

4 is a term since its ternary and balanced ternary representation are both 11 which is a palindrome.
16 is a term since its ternary representation is 121 and its balanced ternary representation (with 2 standing for the -1 digit) is 1221, and both are palindromes.

Mathematica

Select[Range[0, 10^4], PalindromeQ[IntegerDigits[#, 3]] && PalindromeQ @ balTernDigits[#] &] (* using balTernDigits by Robert G. Wilson v at A134027 *)

Prog

(PARI) is(n) = {my (t=digits(n, 3)); if (t==Vecrev(t), my (b=[], d); while (n, b=concat(d=[0, 1, -1][1+n%3], b); n=(n-d)/3); b==Vecrev(b), 0)} \\ Rémy Sigrist, Jun 10 2022

Crossrefs

Intersection of A014190 and A134027.

Subsequences: A003462, A034472 \ {2}, A354886.

Cf. A007089, A140267.

Sequence in context: A259725 A260936 A043001 * A191195 A310347 A310348

Adjacent sequences: A354882 A354883 A354884 * A354886 A354887 A354888

Keyword

nonn,base

Author

Amiram Eldar, Jun 10 2022

Status

approved