A024773 -id:A024773 - cp's OEIS frontend

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

Onno M. Cain, Nov 26 2019

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).

			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.

Onno M. Cain, Python Code

Cf. A024773, A085823, A085822, A213300.

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 *)

Python
```
# see Cain link
```

cp's OEIS Frontend

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

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