A282666 The larger term of the pair (a(n), a(n+1)) is always prime and the larger digit of any pair of adjacent digits is also prime.

0, 2, 1, 3, 5, 4, 7, 6, 71, 20, 23, 12, 13, 17, 15, 31, 21, 37, 22, 53, 25, 47, 27, 67, 30, 73, 32, 127, 33, 131, 35, 137, 45, 151, 50, 223, 51, 227, 52, 157, 54, 503, 55, 173, 57, 233, 70, 251, 72, 257, 74, 521, 75, 271, 76, 727, 77, 277, 120, 307, 121, 313, 122, 317, 123, 331, 202, 337, 125, 353, 130, 373, 132, 523, 133, 547, 135

Offset

1,2

Comments

The sequence is started with a(1) = 0 and always extended with the smallest integer not yet present and not leading to a contradiction.

If two successive digits are equal (e.g., 2,2) we accept that there is a "larger one" (2).

The digits "8" and "9" cannot be present in the sequence as no "prime digit" is larger than "8" or "9".

Links

Jean-Marc Falcoz, Table of n, a(n) for n = 1..7853

Example

In the 1st pair of integers (0,2) the larger term is 2, which is prime;
in the 2nd pair of integers (2,1) the larger term is 2, which is prime;
in the 3rd pair of integers (1,3) the larger term is 3, which is prime;
in the 4th pair of integers (3,5) the larger term is 5, which is prime;
...
in the 9th pair of integers (71,20) the larger term is 71, which is prime;
in the 10th pair of integers (20,23) the larger term is 23, which is prime;
in the 11th pair of integers (23,12) the larger term is 23, which is prime; etc.
In the 1st pair of digits (0,2) the larger digit is 2, which is prime;
in the 2nd pair of digits (2,1) the larger digit is 2, which is prime;
in the 3rd pair of digits (1,3) the larger digit is 3, which is prime;
in the 4th pair of digits (3,5) the larger digit is 5, which is prime;
...
in the 9th pair of digits (7,1) the larger digit is 7, which is prime;
in the 10th pair of digits (1,2) the larger digit is 2, which is prime;
in the 11th pair of digits (2,0) the larger digit is 2, which is prime; etc.

Crossrefs

Sequence in context: A234751 A113790 A181094 * A181560 A250103 A063705

Adjacent sequences: A282663 A282664 A282665 * A282667 A282668 A282669

Keyword

nonn,base

Author

Eric Angelini and Jean-Marc Falcoz, Feb 20 2017

Status

approved