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A352319 Numbers whose minimal (or greedy) Pell representation (A317204) is palindromic.

%I A352319 #8 Mar 14 2022 02:42:51
%S A352319 0,1,3,6,8,13,20,30,35,40,44,49,71,88,102,119,170,182,194,204,216,238,
%T A352319 242,254,266,276,288,409,450,484,525,559,580,621,655,696,986,1015,
%U A352319 1044,1068,1097,1150,1160,1189,1218,1242,1271,1334,1363,1392,1396,1425,1454
%N A352319 Numbers whose minimal (or greedy) Pell representation (A317204) is palindromic.
%C A352319 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 A352319 A048739 is a subsequence since these are repunit numbers in the minimal Pell representation.
%C A352319 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 A352319 Amiram Eldar, <a href="/A352319/b352319.txt">Table of n, a(n) for n = 1..10000</a>
%e A352319 The first 10 terms are:
%e A352319    n  a(n)  A317204(a(n))
%e A352319   --  ----  -------------
%e A352319    1     0              0
%e A352319    2     1              1
%e A352319    3     3             11
%e A352319    4     6            101
%e A352319    5     8            111
%e A352319    6    13           1001
%e A352319    7    20           1111
%e A352319    8    30          10001
%e A352319    9    35          10101
%e A352319   10    40          10201
%t A352319 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 A352319 Cf. A000129, A317204.
%Y A352319 Subsequences: A001109, A048739, A052937 \ {2}.
%Y A352319 Similar sequences: A002113, A006995, A014190, A094202, A331191, A351712, A351717, A352087.
%K A352319 nonn,base
%O A352319 1,3
%A A352319 _Amiram Eldar_, Mar 12 2022