cp's OEIS Frontend

A361827 For any number k >= 0, let T_k be the triangle whose base corresponds to the ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t = (-u-v) mod 3; this sequence lists the numbers k such that the configurations of 0's, 1's and 2's in T_k are the same up to rotation.

%I A361827 #12 Mar 28 2023 14:01:17
%S A361827 3,5,6,7,11,15,19,21,84,93,102,140,149,158,168,177,186,196,205,214,
%T A361827 308,318,351,377,410,420,528,532,574,588,702,715,2271,2396,2523,2621,
%U A361827 2775,2873,2933,3150,3185,3375,3410,3627,3687,3785,3939,4037,4164,4289,4519
%N A361827 For any number k >= 0, let T_k be the triangle whose base corresponds to the ternary expansion of k (without leading zeros) and other values, say t above u and v, satisfy t = (-u-v) mod 3; this sequence lists the numbers k such that the configurations of 0's, 1's and 2's in T_k are the same up to rotation.
%C A361827 This sequence is a variant of A361818.
%C A361827 If k belongs to the sequence, then A004488(k) belongs to the sequence.
%C A361827 The ternary lengths of terms belong to A007494 (as the number of values in triangles must be divisible by 3).
%C A361827 This sequence is infinite as it contains the numbers whose ternary digits match the regular expression "(210)+".
%C A361827 Empirically, there are 4*3^floor((w-1)/2) terms with w ternary digits.
%C A361827 No term belongs to A297250.
%H A361827 Rémy Sigrist, <a href="/A361827/a361827.png">Triangles illustrating initial terms</a>
%H A361827 Rémy Sigrist, <a href="/A361827/a361827.gp.txt">PARI program</a>
%H A361827 <a href="/index/X#XOR-triangles">Index entries for sequences related to XOR-triangles</a>
%e A361827 The ternary expansion of 149 is "12112", and the corresponding triangle is:
%e A361827             0
%e A361827            1 2
%e A361827           0 2 2
%e A361827          0 0 1 0
%e A361827         1 2 1 1 2
%e A361827 The configurations of 0's, 1's and 2's are the same up to rotation, so 149 belongs to this sequence:
%e A361827             0            .            .
%e A361827            . .          1 .          . 2
%e A361827           0 . .        . . .        . 2 2
%e A361827          0 0 . 0      . . 1 .      . . . .
%e A361827         . . . . .    1 . 1 1 .    . 2 . . 2
%o A361827 (PARI) See Links section.
%Y A361827 Cf. A004488, A007494, A297250, A361818.
%K A361827 nonn,base
%O A361827 1,1
%A A361827 _Rémy Sigrist_, Mar 26 2023