A306311 Lexicographically earliest sequence starting with a(1) = 1 with no duplicate terms such that the n-th digit of the sequence is a divisor of a(n).

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 18, 16, 24, 17, 25, 19, 32, 21, 36, 22, 28, 23, 35, 26, 45, 27, 54, 33, 34, 38, 29, 39, 42, 44, 46, 48, 56, 52, 51, 57, 55, 58, 66, 64, 65, 62, 49, 75, 68, 63, 69, 72, 76, 78, 88, 74, 81, 84, 99, 92, 82, 96, 112, 116, 114, 124, 128, 85, 126, 95, 86, 115, 31, 125, 77, 135, 145, 155

Offset

1,2

Comments

This sequence is a derangement of the zeroless numbers; any 0 digit in a(n) would force a division by zero later in the sequence.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..20010

Example

The sequence starts with 1,2,3,4,5,6,7,8,9,11,12,13,14,15,18,16,24,17,25,19,32,21,...
The first nine terms speak for themselves;
the 10th digit of the sequence is 1 and 1 is a divisor of a(10) = 11;
the 11th digit of the sequence is 1 and 1 is a divisor of a(11) = 12;
the 12th digit of the sequence is 1 and 1 is a divisor of a(12) = 13;
the 13th digit of the sequence is 2 and 2 is a divisor of a(13) = 14;
the 14th digit of the sequence is 1 and 1 is a divisor of a(14) = 15;
the 15th digit of the sequence is 3 and 3 is a divisor of a(15) = 18;
etc.

Crossrefs

Cf. A052382 (the zeroless numbers).

Sequence in context: A052044 A253643 A050743 * A028964 A219361 A191878

Adjacent sequences: A306308 A306309 A306310 * A306312 A306313 A306314

Keyword

base,nonn

Author

Eric Angelini and Jean-Marc Falcoz, Feb 06 2019

Status

approved