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A308711 Left-truncatable primes in base-10 bijective numeration.

%I A308711 #22 Jun 25 2025 08:06:41
%S A308711 2,3,5,7,13,17,23,37,43,47,53,67,73,83,97,103,107,113,137,167,173,197,
%T A308711 223,283,307,313,317,337,347,353,367,373,383,397,443,467,503,523,547,
%U A308711 607,613,617,643,647,653,673,683,743,773,797,823,853,883,907,937,947,953,967,983,997
%N A308711 Left-truncatable primes in base-10 bijective numeration.
%C A308711 Not identical to A033664; in fact a strict subsequence of A033664. For example, 2003 belongs to A033664 but not to this sequence, since in bijective numerals 2003 is 19X3, whose suffix 9X3 = 1003 = 17 * 59.
%H A308711 Robin Houston, <a href="/A308711/b308711.txt">Table of n, a(n) for n = 1..8391</a>
%H A308711 Wikipedia, <a href="https://en.wikipedia.org/wiki/Bijective_numeration">Bijective numeration</a>
%o A308711 (Sage)
%o A308711 DIGITS = "123456789X"
%o A308711 DECODE = {d: i + 1 for i, d in enumerate(DIGITS)}
%o A308711 def decode(s):
%o A308711     return reduce(lambda n, c: 10 * n + DECODE[c], s, 0)
%o A308711 def search(s):
%o A308711     n = decode(s)
%o A308711     if n > 0:
%o A308711         if not is_prime(n): return
%o A308711         yield n
%o A308711     for digit in DIGITS: yield from search(digit + s)
%o A308711 full = sorted(search(""))
%o A308711 full[:10]
%Y A308711 Cf. A024785, A033664.
%K A308711 nonn,base,easy,fini,full
%O A308711 1,1
%A A308711 _Robin Houston_, Jun 19 2019