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A330672
Numbers whose base phi representation is symmetrical with respect to the radix point.
3
0, 2, 14, 36, 38, 94, 96, 246, 248, 260, 644, 646, 658, 680, 682, 1686, 1688, 1700, 1722, 1724, 1780, 1782, 4414, 4416, 4428, 4450, 4452, 4508, 4510, 4660, 4662, 4674, 11556, 11558, 11570, 11592, 11594, 11650, 11652, 11802, 11804, 11816, 12200, 12202, 12214
OFFSET
1,2
COMMENTS
There is a 13-state finite automaton that accepts the Zeckendorf expansions of the members of this sequence. - Jeffrey Shallit, May 03 2023
LINKS
Jeffrey Shallit, Proving Properties of phi-Representations with the Walnut Theorem-Prover, arXiv:2305.02672 [math.NT], 2023.
FORMULA
A130600(a(n)) belongs to A057148 for any n >= 0.
EXAMPLE
The first terms, alongside their base phi representation, are:
n a(n) phi(a(n))
-- ---- -------------------------
1 0 0.0
2 2 10.01
3 14 100100.001001
4 36 10010000.00001001
5 38 10010010.01001001
6 94 1001000000.0000001001
7 96 1001000010.0100001001
8 246 100100000000.000000001001
9 248 100100000010.010000001001
10 260 100100100100.001001001001
PROG
(PARI) See Links section.
CROSSREFS
See A330722 for a weaker variant.
Sequence in context: A367578 A134647 A004117 * A135706 A091520 A338327
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, Apr 23 2020
STATUS
approved