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

2, 3, 5, 7, 13, 17, 23, 37, 43, 47, 53, 67, 73, 83, 97, 103, 107, 113, 137, 167, 173, 197, 223, 283, 307, 313, 317, 337, 347, 353, 367, 373, 383, 397, 443, 467, 503, 523, 547, 607, 613, 617, 643, 647, 653, 673, 683, 743, 773, 797, 823, 853, 883, 907, 937, 947, 953, 967, 983, 997

Offset: 1

Author

Robin Houston, Jun 19 2019

Keywords

• nonn
• base
• easy
• fini
• full

Comments

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.

Links

• Robin Houston, Table of n, a(n) for n = 1..8391
• Wikipedia, Bijective numeration

Crossrefs

Cf. A024785, A033664.

Programs

Sage

DIGITS = "123456789X"
DECODE = {d: i + 1 for i, d in enumerate(DIGITS)}
def decode(s):
    return reduce(lambda n, c: 10 * n + DECODE[c], s, 0)
def search(s):
    n = decode(s)
    if n > 0:
        if not is_prime(n): return
        yield n
    for digit in DIGITS: yield from search(digit + s)
full = sorted(search(""))
full[:10]