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

Offset

1,1

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

Prog

(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]

Crossrefs

Cf. A024785, A033664.

Sequence in context: A234695 A067905 A042993 * A033664 A024785 A069866

Adjacent sequences: A308708 A308709 A308710 * A308712 A308713 A308714

Keyword

nonn,base,easy,fini,full

Author

Robin Houston, Jun 19 2019

Status

approved