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