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A352507 Number whose representation in the base of Catalan numbers (A014418) is palindromic.

%I A352507 #11 Apr 01 2022 11:38:04
%S A352507 0,1,3,6,8,15,22,43,48,53,59,64,69,133,152,171,177,196,215,430,444,
%T A352507 458,477,491,505,524,538,552,564,578,592,611,625,639,658,672,686,1431,
%U A352507 1487,1543,1568,1624,1680,1705,1761,1817,1862,1918,1974,1999,2055,2111,2136
%N A352507 Number whose representation in the base of Catalan numbers (A014418) is palindromic.
%C A352507 The partial sums of the Catalan numbers with positive index (A014138) are terms, since the representation of A014138(n) is n 1's.
%H A352507 Amiram Eldar, <a href="/A352507/b352507.txt">Table of n, a(n) for n = 1..10000</a>
%e A352507 The first 10 terms are:
%e A352507    n  a(n)  A014418(a(n))
%e A352507   --  ----  -------------
%e A352507    1     0              0
%e A352507    2     1              1
%e A352507    3     3             11
%e A352507    4     6            101
%e A352507    5     8            111
%e A352507    6    15           1001
%e A352507    7    22           1111
%e A352507    8    43          10001
%e A352507    9    48          10101
%e A352507   10    53          10201
%t A352507 c[n_] := c[n] = CatalanNumber[n]; q[n_] := Module[{s = {}, m = n, i}, While[m > 0, i = 1; While[c[i] <= m, i++]; i--; m -= c[i]; AppendTo[s, i]]; PalindromeQ @ IntegerDigits[Total[4^(s - 1)], 4]]; Select[Range[0, 2000], q]
%Y A352507 Cf. A000108, A014418.
%Y A352507 Subsequences: A014138, A141351 \ {2}.
%Y A352507 Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087, A352105, A352319, A352341.
%K A352507 nonn,base
%O A352507 1,3
%A A352507 _Amiram Eldar_, Mar 19 2022