A336035 -id:A336035

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A336034

The rightmost digit d of a(n) jumps over d digits to the right and is duplicated there. Lexicographically earliest sequence of distinct positive integers with this property.

+10
3

1, 2, 11, 21, 3, 12, 4, 322, 5, 42, 6, 7, 251, 8, 161, 71, 9, 13, 82, 1322, 19, 22, 14, 24, 15, 49, 43, 151, 31, 41, 91, 51, 61, 81, 111, 112, 16, 23, 17, 33, 62, 53, 27, 63, 18, 73, 37, 83, 25, 831, 715, 26, 28, 35, 29, 64, 158, 34, 36, 93, 44

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

No term ends in 0 as this would force the next integer to start with zero.

LINKS

Carole Dubois, Table of n, a(n) for n = 1..5000

EXAMPLE

The rightmost digit of a(1) = 1 is 1; we duplicate this digit in position 3;

The rightmost digit of a(2) = 2 is 2; we duplicate this digit in position 5;

The rightmost digit of a(3) = 11 is 1; we duplicate this digit in position 6;

The rightmost digit of a(4) = 21 is 1; we duplicate this digit in position 8;

The rightmost digit of a(5) = 3 is 3; we duplicate this digit in position 11; etc.

CROSSREFS

Cf. A336035 (duplication of the leftmost digit of a(n) to the left), A336036 (first and last digits of a(n) are duplicated respectively to the left and to the right).

KEYWORD

base,nonn

AUTHOR

Eric Angelini and Carole Dubois, Jul 05 2020

STATUS

approved

A336036

The leftmost digit L of a(n) jumps over L+1 digits to the left and is duplicated there; the rightmost digit R of a(n) jumps over R digits to the right and is duplicated there. Lexicographically earliest sequence of distinct positive integers with this property and a(1) = 11.

+10
3

11, 1, 111, 112, 12, 21, 2, 13, 201, 3, 14, 1301, 4, 15, 16, 401, 5, 17, 601, 512, 172, 51, 211, 113, 18, 1311, 114, 1801, 411, 115, 19, 101, 511, 116, 911, 117, 611, 118, 1711, 119, 1811, 1112, 19201, 212, 22, 23, 202, 31, 213, 102, 32, 24, 203, 241, 311, 412, 1221, 214, 204, 242, 24201, 215, 205, 25, 501

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

No term ends in 0 as this would force the next integer to start with zero.

LINKS

Carole Dubois, Table of n, a(n) for n = 1..5000

EXAMPLE

The sequence starts with 11, 1, 111, 112, 12, 21, 2, 13, 201, 3,...

We don't duplicate to the left the leftmost digit of a(1) = 11 as there is no room.

The rightmost digit of a(1) = 11 is 1; we duplicate this digit in position 4;

The leftmost digit of a(2) = 1 is 1; we duplicate this digit in position 1;

The rightmost digit of a(2) = 1 is 1; we duplicate this digit in position 5;

The leftmost digit of a(3) = 111 is 1; we duplicate this digit in position 2;

The rightmost digit of a(3) = 111 is 1; we duplicate this digit in position 8;

The leftmost digit of a(4) = 112 is 1; we duplicate this digit in position 5;

The rightmost digit of a(4) = 112 is 2; we duplicate this digit in position 12;

The leftmost digit of a(5) = 12 is 1; we duplicate this digit in position 8;

The rightmost digit of a(5) = 12 is 2; we duplicate this digit in position 14;

The leftmost digit of a(6) = 21 is 2; we duplicate this digit in position 9; etc.