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A364378 Numbers whose representation in Jacobsthal greedy base (A265747) is palindromic.

%I A364378 #8 Jul 29 2023 03:21:55
%S A364378 0,1,2,4,6,9,12,20,22,27,36,41,44,60,68,84,86,97,112,123,132,143,158,
%T A364378 169,172,204,220,252,260,292,308,340,342,363,396,417,432,453,486,507,
%U A364378 516,537,570,591,606,627,660,681,684,748,780,844,860,924,956,1020,1028
%N A364378 Numbers whose representation in Jacobsthal greedy base (A265747) is palindromic.
%C A364378 A128209(n) = A001045(n) + 1 is a term for n >= 3, since its representation is two 1's with n-3 0's between them.
%C A364378 A084639(n) is a term for n >= 1 since its representation is n 1's.
%C A364378 A014825(n) is a term for n >= 1 since its representation is n-1 0's interleaved with n 1's.
%H A364378 Amiram Eldar, <a href="/A364378/b364378.txt">Table of n, a(n) for n = 1..10000</a>
%e A364378 The first 10 terms are:
%e A364378    n  a(n)  A265747(a(n))
%e A364378   --  ----  -------------
%e A364378    1     0              0
%e A364378    2     1              1
%e A364378    3     2              2
%e A364378    4     4             11
%e A364378    5     6            101
%e A364378    6     9            111
%e A364378    7    12           1001
%e A364378    8    20           1111
%e A364378    9    22          10001
%e A364378   10    27          10101
%t A364378 palJacobQ[n_] := PalindromeQ[A265747[n]]; Select[Range[0, 1000], palJacobQ] (* using A265747[n] *)
%o A364378 (PARI) is(n) = {my(dig = digits(A265747(n))); dig == Vecrev(dig);} \\ using A265747(n)
%Y A364378 Cf. A001045, A014825, A084639, A128209, A265747.
%Y A364378 Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087, A352105, A352319, A352341, A364214.
%K A364378 nonn,base
%O A364378 1,3
%A A364378 _Amiram Eldar_, Jul 21 2023