A355313 - OEIS

%I #26 Aug 23 2022 10:37:07

%S 65,67,75,85,96,130,134,150,170,192,195,225,255,288,300,327,340,375,

%T 381,425,433,443,450,456,487,510,525,595,600,654,665,667,675,680,750,

%U 762,765,795,825,886,895,900,912,927,974,975,981,996,1050,1125,1139,1200,1275,1277,1308,1330,1334,1340,1350,1368,1535,1543,1590

%N Numbers that can be written as reversals in two different bases, where the bases are also reversals. (Trailing zeros are allowed.)

%C Numbers that use trailing zeros are included in this sequence. See the last two examples.

%C Proved to be infinite by Álvaro Lozano-Robledo.

%H Jordan Canevari, <a href="/A355313/a355313.txt">Generating Python program</a>

%H Jordan Canevari, <a href="/A355313/a355313_1.txt">Data for each term in sequence</a>

%H Á. Lozano-Robledo and J. Canevari, <a href="https://www.tiktok.com/@mathandcobb/video/7110667721133690158">Proof that the sequence is infinite</a>

%e 65  = (4,1)_16   = (1,4)_61;

%e 134 = (10,4)_13  = (4,10)_31;

%e 443 = (13:1)_34  = (1:13)_430;

%e 456 = (1,5,0)_19 = (5,1)_91.

%o (Python) See Canevari link

%Y A354474 is a subsequence.

%K nonn,base

%O 1,1

%A _Jordan Canevari_, Jun 27 2022