A365781 Lexicographically earliest permutation of the composite numbers such that a(n) - [the next digit] is a prime number.

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

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

Table of n, a(n) for n=1..82.

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

Cf. A365768, A365769, A365780.

Sequence in context: A298264 A014476 A080362 * A298400 A070295 A123483

Adjacent sequences: A365778 A365779 A365780 * A365782 A365783 A365784

Keyword

nonn,easy,base,fini,full

Author

Eric Angelini, Sep 18 2023

Extensions

More terms from David A. Corneth, Sep 18 2023

Status

approved