A330007 Base-24 integers whose substrings are primes (written in base 10).

2, 3, 5, 7, 11, 13, 17, 19, 23, 53, 59, 61, 67, 71, 79, 83, 89, 127, 131, 137, 139, 173, 179, 181, 191, 269, 271, 277, 281, 283, 317, 331, 419, 421, 431, 461, 463, 467, 479, 557, 563, 569, 571, 1279, 1283, 1289, 1291, 1423, 1429, 1433, 1483, 1613, 1619, 1709, 1721, 1723, 1901, 1907, 1997, 1999, 2011, 3061, 3163, 3299

Offset

1,1

Comments

The largest such number is a(103)=266003, which is written (19|5|19|11)_24 in base 24.

We might call these numbers "substrimes" (= substring-primes) since the term (1) is concise, (2) is pronounceable, and (3) keeps these numbers distinct in communication from different but similar sequences (see Crossrefs).

Links

Table of n, a(n) for n=1..64.

Onno M. Cain, Live Code

Onno M. Cain, Python Code

Example

a(64) = 3299 = (5|17|11)_24 is in the sequence because 5, 17, 11, (5|17)_24=137, (17|11)=419, and 3299 itself are all prime.

Mathematica

With[{b = 24}, Select[Range[b^4], Function[{s, n}, AllTrue[Flatten@ Array[FromDigits[#, b] & /@ Partition[s, #, 1] &, n], PrimeQ]] @@ {#, Length@ #} &@ IntegerDigits[#, b] &]] (* Michael De Vlieger, Dec 15 2019 *)

Prog

(Python) # see Cain link

Crossrefs

Cf. A024773, A085823, A085822, A213300.

Sequence in context: A075239 A255073 A341667 * A008792 A359497 A094746

Adjacent sequences: A330004 A330005 A330006 * A330008 A330009 A330010

Keyword

nonn,base,fini

Author

Onno M. Cain, Nov 26 2019

Status

approved