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A352507
Number whose representation in the base of Catalan numbers (A014418) is palindromic.
2
0, 1, 3, 6, 8, 15, 22, 43, 48, 53, 59, 64, 69, 133, 152, 171, 177, 196, 215, 430, 444, 458, 477, 491, 505, 524, 538, 552, 564, 578, 592, 611, 625, 639, 658, 672, 686, 1431, 1487, 1543, 1568, 1624, 1680, 1705, 1761, 1817, 1862, 1918, 1974, 1999, 2055, 2111, 2136
OFFSET
1,3
COMMENTS
The partial sums of the Catalan numbers with positive index (A014138) are terms, since the representation of A014138(n) is n 1's.
LINKS
EXAMPLE
The first 10 terms are:
n a(n) A014418(a(n))
-- ---- -------------
1 0 0
2 1 1
3 3 11
4 6 101
5 8 111
6 15 1001
7 22 1111
8 43 10001
9 48 10101
10 53 10201
MATHEMATICA
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]
CROSSREFS
Subsequences: A014138, A141351 \ {2}.
Sequence in context: A051212 A143869 A165298 * A117148 A376480 A343272
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 19 2022
STATUS
approved