A322466 Lexicographically first sequence of distinct terms such that the a(n)th digit after a(n) shares a(n)'s parity.

1, 3, 4, 2, 5, 6, 8, 9, 7, 10, 20, 12, 11, 13, 14, 15, 16, 18, 17, 19, 30, 22, 21, 31, 24, 23, 26, 32, 25, 33, 27, 28, 34, 35, 29, 36, 38, 37, 39, 50, 40, 51, 41, 42, 52, 44, 53, 43, 45, 54, 46, 55, 47, 48, 49, 56, 57, 58, 59, 60, 62, 61, 63, 70, 64, 65, 66, 72, 67, 71, 68, 73, 69, 74, 75, 76, 78, 80, 77, 79, 81

Offset

1,2

Comments

This sequence is conjectured to be a permutation of the positive integers.

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..15002

Example

The sequence starts with 1,3,4,2,5,6,8,9,7,10,20,12,...
a(1) = 1 forces the next digit to be odd;
Thus a(2) = 3 as this 3 is the smallest available integer not leading to a contradiction; this 3 forces the 3rd digit after 3 to be odd;
Could a(3) be equal to 2 (instead of 4, here)? No, because this would lead to a contradiction as we've just seen that the 3rd digit after 3 must be odd;
Thus a(3) = 4; this 4 forces the 4th digit after 4 to be even;
a(4) = 2 as this 2 is the smallest available integer not leading to a contradiction; this 2 forces the 2nd digit after 2 to be even;
a(5) = 5 as the first digit of a(5) must be odd and 5 is the smallest available integer not leading to a contradiction; this 5 forces the 5th digit after 5 to be odd;
a(6) = 6 as the first digit of a(6) must be even and 6 is the smallest available integer not leading to a contradiction; this 6 forces the 6th digit after 6 to be even;
a(7) = 8 as the first digit of a(7) must be even and 8 is the smallest available integer not leading to a contradiction; this 8 forces the 8th digit after 8 to be even;
Could a(8) be equal to 7 (instead of 9, here)? No, because this would lead to a contradiction as we've just seen that the 8th digit after 8 must be even;
Thus a(8) = 9 as this 9 is the smallest available integer not leading to a contradiction; this 9 forces the 9th digit after 9 to be odd;
a(9) = 7 as this 7 is the smallest available integer not leading to a contradiction; this 7 forces the 7th digit after 7 to be odd;
a(10) = 10 as the smallest available integer starting with an even digit and not leading to a contradiction is 10; this 10 forces the 10th digit after 10 to be even;
a(11) = 20 as the smallest available integer starting with an even digit and not leading to a contradiction is 20; this 20 forces the 10th digit after 20 to be even;
a(12) = 12 as the smallest available integer ending with an even digit and not leading to a contradiction is 12; this 12 forces the 12th digit after 12 to be even;
etc.

Crossrefs

Sequence in context: A197269 A201905 A138609 * A211377 A350218 A056699

Adjacent sequences: A322463 A322464 A322465 * A322467 A322468 A322469

Keyword

base,nonn,look

Author

Eric Angelini and Jean-Marc Falcoz, Dec 09 2018

Status

approved