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%I #8 Mar 14 2022 02:42:51
%S 0,1,3,6,8,13,20,30,35,40,44,49,71,88,102,119,170,182,194,204,216,238,
%T 242,254,266,276,288,409,450,484,525,559,580,621,655,696,986,1015,
%U 1044,1068,1097,1150,1160,1189,1218,1242,1271,1334,1363,1392,1396,1425,1454
%N Numbers whose minimal (or greedy) Pell representation (A317204) is palindromic.
%C A052937(n) = A000129(n+1)+1 is a term for n>0, since its minimal Pell representation is 10...01 with n-1 0's between two 1's.
%C A048739 is a subsequence since these are repunit numbers in the minimal Pell representation.
%C A001109 is a subsequence. The minimal Pell representation of A001109(n), for n>1, is 1010...01, with n-1 0's interleaved with n 1's.
%H Amiram Eldar, <a href="/A352319/b352319.txt">Table of n, a(n) for n = 1..10000</a>
%e The first 10 terms are:
%e n a(n) A317204(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 13 1001
%e 7 20 1111
%e 8 30 10001
%e 9 35 10101
%e 10 40 10201
%t pell[1] = 1; pell[2] = 2; pell[n_] := pell[n] = 2*pell[n - 1] + pell[n - 2]; q[n_] := Module[{s = {}, m = n, k}, While[m > 0, k = 1; While[pell[k] <= m, k++]; k--; AppendTo[s, k]; m -= pell[k]; k = 1]; PalindromeQ[IntegerDigits[Total[3^(s - 1)], 3]]]; Select[Range[0, 1500], q]
%Y Cf. A000129, A317204.
%Y Subsequences: A001109, A048739, A052937 \ {2}.
%Y Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087.
%K nonn,base
%O 1,3
%A _Amiram Eldar_, Mar 12 2022