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A362755 Irregular triangle read by rows; the n-th row lists the numbers k such that if phi^e appears in the base phi expansion of k then phi^e also appears in the base phi expansion of n (where phi denotes A001622, the golden ratio).

%I A362755 #11 May 08 2023 09:36:04
%S A362755 0,0,1,0,2,0,3,0,1,3,4,0,5,0,6,0,7,0,1,7,8,0,2,7,9,0,3,7,10,0,1,3,4,7,
%T A362755 8,10,11,0,12,0,13,0,14,0,1,14,15,0,16,0,17,0,18,0,1,18,19,0,2,18,20,
%U A362755 0,3,18,21,0,1,3,4,18,19,21,22,0,5,18,23,0,6,18,24
%N A362755 Irregular triangle read by rows; the n-th row lists the numbers k such that if phi^e appears in the base phi expansion of k then phi^e also appears in the base phi expansion of n (where phi denotes A001622, the golden ratio).
%C A362755 See A361755 for a similar sequence.
%H A362755 Rémy Sigrist, <a href="/A362755/b362755.txt">Table of n, a(n) for n = 0..9999</a> (rows for n = 0..1060 flattened)
%H A362755 Rémy Sigrist, <a href="/A362755/a362755.gp.txt">PARI program</a>
%H A362755 Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>
%F A362755 T(n, 1) = 0.
%F A362755 T(n, 2) = 1 iff n belongs to A214971.
%e A362755 Triangle begins:
%e A362755   n   n-th row
%e A362755   --  ------------------------
%e A362755    0  0
%e A362755    1  0, 1
%e A362755    2  0, 2
%e A362755    3  0, 3
%e A362755    4  0, 1, 3, 4
%e A362755    5  0, 5
%e A362755    6  0, 6
%e A362755    7  0, 7
%e A362755    8  0, 1, 7, 8
%e A362755    9  0, 2, 7, 9
%e A362755   10  0, 3, 7, 10
%e A362755   11  0, 1, 3, 4, 7, 8, 10, 11
%e A362755   12  0, 12
%e A362755   13  0, 13
%e A362755   14  0, 14
%e A362755   15  0, 1, 14, 15
%o A362755 (PARI) See Links section.
%Y A362755 Cf. A001622, A104605, A214971, A361755.
%K A362755 nonn,base,tabf
%O A362755 0,5
%A A362755 _Rémy Sigrist_, May 02 2023