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A352319
Numbers whose minimal (or greedy) Pell representation (A317204) is palindromic.
8
0, 1, 3, 6, 8, 13, 20, 30, 35, 40, 44, 49, 71, 88, 102, 119, 170, 182, 194, 204, 216, 238, 242, 254, 266, 276, 288, 409, 450, 484, 525, 559, 580, 621, 655, 696, 986, 1015, 1044, 1068, 1097, 1150, 1160, 1189, 1218, 1242, 1271, 1334, 1363, 1392, 1396, 1425, 1454
OFFSET
1,3
COMMENTS
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.
A048739 is a subsequence since these are repunit numbers in the minimal Pell representation.
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.
LINKS
EXAMPLE
The first 10 terms are:
n a(n) A317204(a(n))
-- ---- -------------
1 0 0
2 1 1
3 3 11
4 6 101
5 8 111
6 13 1001
7 20 1111
8 30 10001
9 35 10101
10 40 10201
MATHEMATICA
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]
CROSSREFS
Subsequences: A001109, A048739, A052937 \ {2}.
Sequence in context: A346597 A108161 A263349 * A297211 A365314 A345318
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 12 2022
STATUS
approved