login
A330007
Base-24 integers whose substrings are primes (written in base 10).
1
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
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