A336668 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.

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, 66, 68, 77, 80, 82, 84, 86, 88, 99, 111, 222, 300, 303, 306, 309, 330, 333, 336, 339, 360, 363, 366, 369, 390, 393, 396, 399, 444, 555, 600, 603, 606, 609, 630, 633

Offset: 1

Author

Rémy Sigrist, Jul 29 2020

Keywords

• nonn
• base

Comments

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).

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

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

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

Examples

			We can arrange the decimal digits of 46064686 around a circle as follows:
.               4
.         6           6
.
.
.      8                 0
.
.
.         6           6
.               4
- moving clockwise:
   - the digit 4 in the north leads to the digit 4 in the south and vice versa,
   - the digit 6 in the northeast leads to the digit 6 in the northwest,
   - the digit 6 in the northwest leads to the digit 6 in the southwest,
   - the digit 6 in the southwest leads to the digit 6 in the southeast,
   - the digit 6 in the southeast leads to the digit 6 in the northeast,
   - the digit 0 leads to itself,
   - the digit 8 leads to itself (after a full turn),
- so 46064686 belongs to this sequence.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, PARI program for A336668

Crossrefs

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

Programs

PARI

See Links section.