A336880 Numbers with decimal expansion d_1, ..., d_w such that for any k in 1..w there is some m in 1..w such that d_k = d_m = abs(k - m).

0, 11, 110, 111, 202, 1100, 1110, 1111, 2020, 2222, 3003, 3113, 11000, 11011, 11100, 11110, 11111, 11202, 20200, 20202, 20211, 22220, 22222, 23203, 30030, 30232, 31130, 33033, 40004, 40114, 41104, 41114, 42024, 110000, 110011, 110110, 110111, 110202, 111000

Offset: 1

Author

Rémy Sigrist, Aug 06 2020

Keywords

• nonn
• base

Comments

This sequence has similarities with A336668.

All repunits (A002275) belong to this sequence.

The concatenation of two terms is also a term.

The digit reversal (A004086) of a term is also a term.

For any d in 1..9, d * (1 + 10^d) is the first term containing the digit d.

Examples

			Regarding 30232:
- the first digit 3 is 3 positions away from the second digit 3 and vice versa,
- the digit 0 matches itself,
- the first digit 2 is 2 positions away from the second digit 2 and vice versa,
- so 30232 belongs to this sequence.
		

Links

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

Crossrefs

Cf. A002275, A144795 (binary analog), A336668.

Programs

PARI

is(n, base=10) = { my (d=digits(n, base)); for (k=1, #d, if ((k-d[k]<1 || d[k-d[k]]!=d[k]) && (k+d[k]>#d || d[k+d[k]]!=d[k]), return (0)));
return (1) }