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%I #13 Jan 13 2019 03:09:56
%S 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,
%T 73,32,127,33,131,35,137,45,151,50,223,51,227,52,157,54,503,55,173,57,
%U 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
%N 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.
%C The sequence is started with a(1) = 0 and always extended with the smallest integer not yet present and not leading to a contradiction.
%C If two successive digits are equal (e.g., 2,2) we accept that there is a "larger one" (2).
%C The digits "8" and "9" cannot be present in the sequence as no "prime digit" is larger than "8" or "9".
%H Jean-Marc Falcoz, <a href="/A282666/b282666.txt">Table of n, a(n) for n = 1..7853</a>
%e In the 1st pair of integers (0,2) the larger term is 2, which is prime;
%e in the 2nd pair of integers (2,1) the larger term is 2, which is prime;
%e in the 3rd pair of integers (1,3) the larger term is 3, which is prime;
%e in the 4th pair of integers (3,5) the larger term is 5, which is prime;
%e ...
%e in the 9th pair of integers (71,20) the larger term is 71, which is prime;
%e in the 10th pair of integers (20,23) the larger term is 23, which is prime;
%e in the 11th pair of integers (23,12) the larger term is 23, which is prime; etc.
%e In the 1st pair of digits (0,2) the larger digit is 2, which is prime;
%e in the 2nd pair of digits (2,1) the larger digit is 2, which is prime;
%e in the 3rd pair of digits (1,3) the larger digit is 3, which is prime;
%e in the 4th pair of digits (3,5) the larger digit is 5, which is prime;
%e ...
%e in the 9th pair of digits (7,1) the larger digit is 7, which is prime;
%e in the 10th pair of digits (1,2) the larger digit is 2, which is prime;
%e in the 11th pair of digits (2,0) the larger digit is 2, which is prime; etc.
%K nonn,base
%O 1,2
%A _Eric Angelini_ and _Jean-Marc Falcoz_, Feb 20 2017
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