

A365781


Lexicographically earliest permutation of the composite numbers such that a(n)  [the next digit] is a prime number.


2



4, 10, 8, 6, 12, 9, 20, 14, 15, 21, 22, 30, 16, 32, 18, 50, 33, 24, 51, 40, 34, 35, 42, 52, 54, 70, 36, 55, 25, 26, 38, 72, 56, 39, 27, 44, 74, 75, 28, 57, 45, 46, 58, 500, 90, 76, 91, 80, 77, 48, 78, 501, 200, 92, 93, 49, 60, 100, 300, 700, 94, 502, 301, 81, 82, 95, 62, 96, 702, 102, 104, 105, 84, 106, 98, 99, 201, 85, 63, 202, 302, 900
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OFFSET

1,1


COMMENTS

Is this sequence finite?
Yes, the sequence is finite. The last term is 900 as the previous prime before 900 is 887 and so the first digit of any next term is too small to reach 887.  David A. Corneth, Sep 18 2023


LINKS



EXAMPLE

a(1) = 4 and 4  1 = 3 (prime);
a(2) = 10 and 10  8 = 2 (prime);
a(3) = 8 and 8  6 = 2 (prime);
a(4) = 6 and 6  1 = 5 (prime);
a(5) = 12 and 12  9 = 3 (prime); etc.


PROG

(PARI) sequence() = {my(res = List([4]), n = 900, leftover = vector(n, i, 1), proceed = 1); leftover[1] = 0; leftover[4] = 0; forprime(p = 2, n, leftover[p] = 0); while(proceed, for(i = 1, n, if(leftover[i] && isprime(res[#res]  digits(i)[1]), listput(res, i); leftover[i] = 0; next(2))); proceed = 0); res} \\ David A. Corneth, Sep 18 2023


CROSSREFS



KEYWORD

nonn,easy,base,fini,full


AUTHOR



EXTENSIONS



STATUS

approved



