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%I #8 Apr 01 2022 11:38:16
%S 1,4,5,9,32,44,55,56,134,144,145,146,155,184,234,324,329,414,426,429,
%T 434,455,511,512,603,636,930,1004,1014,1160,1183,1215,1287,1308,1448,
%U 1472,1505,1562,1595,1808,1854,1967,1985,1995,2051,2075,2096,2135,2165,2255
%N Numbers k such that k and k+1 are both Catalan-Niven numbers (A352508).
%H Amiram Eldar, <a href="/A352509/b352509.txt">Table of n, a(n) for n = 1..10000</a>
%e 4 is a term since 4 and 5 are both Catalan-Niven numbers: the Catalan representation of 4, A014418(20) = 20, has the sum of digits 2+0 = 2 and 4 is divisible by 2, and the Catalan representation of 5, A014418(5) = 100, has the sum of digits 1+0+0 = 1 and 5 is divisible by 1.
%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]]; Divisible[n, Plus @@ IntegerDigits[Total[4^(s - 1)], 4]]]; Select[Range[2300], q[#] && q[#+1] &]
%Y Cf. A000108, A014418, A014420.
%Y Subsequence of A352508.
%Y Subsequences: A038003, A352510, A352511.
%Y Similar sequences: A330927, A328205, A328209, A328213, A330931, A331086, A333427, A334309, A331820, A342427, A344342, A351715, A351720, A352090, A352108, A352321, A352343.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Mar 19 2022