login
Lexicographically earliest sequence of distinct nonprime terms that turns into a sequence of distinct prime numbers when the "slide the digits, don't touch the commas" operation is applied (see the Comments and Example sections).
3

%I #18 Dec 16 2019 11:55:50

%S 1,12,15,111,3633,28,9,14,314,114,611,514,3332,4,18,112,312,1313,138,

%T 33,38,213,183,332,6,1315,2812,215,212,3141,1317,8,315,148,3635,316,

%U 3636,319,3438,2115,1813,831,21,3831,24,511,1316,6313,231,35,8113,836,5313,636,3639,23631,26,39,3837,41856,56,412

%N Lexicographically earliest sequence of distinct nonprime terms that turns into a sequence of distinct prime numbers when the "slide the digits, don't touch the commas" operation is applied (see the Comments and Example sections).

%C Even digits "e" must slide "e" positions to the left; odd digits "o" must slide "o" positions to the right. Commas must stay where they are.

%C Maximum value for terms 1-500 is 8481315. Statistics of digits 0-9 for terms 1-500 is (0, 508, 147, 600, 180, 229, 207, 43, 212, 23). _Lars Blomberg_, Dec 16 2019

%H Lars Blomberg, <a href="/A330367/b330367.txt">Table of n, a(n) for n = 1..500</a>

%e To understand the operation described in the Comments section, we superpose hereunder S and T, S being this sequence and T the result of the said operation:

%e S = 1, 12, 15, 111, 3633, 28, 9, 14, 314, 114, 611, ...

%e T = 2, 11, 61, 811, 1523, 43, 3, 41, 641, 311, 941, ...

%e The first digit "1" of S is now the first digit of 11 in T;

%e the second digit "1" of S is now the second digit of 11 in T;

%e the first digit "2" of S is now the first digit of T;

%e the first digit "1" of 15 in S is now the last digit of 61 in T;

%e the first digit "5" of S is now the second digit of 1523 in T, etc.

%e All terms of S are distinct and nonprimes, all terms of T are distinct and primes. The commas stayed where they were.

%K nonn,base

%O 1,2

%A _Eric Angelini_ and _Lars Blomberg_, Dec 12 2019

%E Corrected a(55) and onwards by _Lars Blomberg_, Dec 16 2019