A384744 Numbers in which all substrings in base 16 are primes.

2, 3, 5, 7, 11, 13, 37, 43, 53, 59, 61, 83, 179, 181, 211, 691, 947, 3389

Offset

1,1

Comments

Terms are formed starting from single digit primes, in base 16, and extending successively with a further prime digit(s) so long as all new substrings are prime.

Following this procedure exhaustively shows the sequence is finite and complete.

Links

Table of n, a(n) for n=1..18.

Codewars, Sliceprime

Yuri Urvantsev, Python program

Example

0x2B3 (691) is a term, because 2, 0xB (11), 3, 0x2B (43), 0xB3 (179), and 0x2B3 (691) are prime.

Prog

(Python) # see links

Crossrefs

Cf. A085823 (for base 10).

Sequence in context: A262377 A237600 A228199 * A128292 A140464 A037174

Adjacent sequences: A384741 A384742 A384743 * A384745 A384746 A384747

Keyword

base,easy,fini,full,nonn

Author

Yuri Urvantsev, Jun 08 2025

Status

approved