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
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
KEYWORD
nonn,base,fini
AUTHOR
Onno M. Cain, Nov 26 2019
STATUS
approved