A336668 - OEIS

%I #18 Jan 11 2021 23:22:02

%S 0,1,2,3,4,5,6,7,8,9,11,20,22,24,26,28,33,40,42,44,46,48,55,60,62,64,

%T 66,68,77,80,82,84,86,88,99,111,222,300,303,306,309,330,333,336,339,

%U 360,363,366,369,390,393,396,399,444,555,600,603,606,609,630,633

%N Numbers with decimal expansion d_1, ..., d_w such that d_k = d*_{k + d_k} for k = 1..w where d* is the w-periodic sequence with initial terms d_1, ..., d_w.

%C In other words, arranging the decimal digits of a term clockwise around a circle, any digit d, say at position p, appears at position p + d (or equivalently at position p - d).

%C All repunits (A002275) appear in this sequence, and they are the only terms with a digit 1.

%C All numbers with repeated digits (A010785) also appear in this sequence.

%C If m > 0 belongs to the sequence, then A020338(m) and A074842(m) also belong to the sequence.

%H Rémy Sigrist, <a href="/A336668/b336668.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A336668/a336668.gp.txt">PARI program for A336668</a>

%e We can arrange the decimal digits of 46064686 around a circle as follows:

%e .               4

%e .         6           6

%e .

%e .

%e .      8                 0

%e .

%e .

%e .         6           6

%e .               4

%e - moving clockwise:

%e    - the digit 4 in the north leads to the digit 4 in the south and vice versa,

%e    - the digit 6 in the northeast leads to the digit 6 in the northwest,

%e    - the digit 6 in the northwest leads to the digit 6 in the southwest,

%e    - the digit 6 in the southwest leads to the digit 6 in the southeast,

%e    - the digit 6 in the southeast leads to the digit 6 in the northeast,

%e    - the digit 0 leads to itself,

%e    - the digit 8 leads to itself (after a full turn),

%e - so 46064686 belongs to this sequence.

%o (PARI) See Links section.

%Y Cf. A002275, A010785, A020338, A074842, A336669.

%K nonn,base

%O 1,3

%A _Rémy Sigrist_, Jul 29 2020