A076586 Total number of right truncatable primes in base n.

0, 4, 7, 14, 36, 19, 68, 68, 83, 89, 179, 176, 439, 373, 414, 473, 839, 1010, 1577, 2271, 2848, 1762, 3376, 5913, 6795, 6352, 10319, 5866, 14639, 13303, 19439, 29982, 38956, 39323, 58857, 41646, 68371, 80754, 128859, 81453, 175734, 161438, 228543, 396274, 538797

Offset: 2

Author

Martin Renner, Oct 20 2002, Sep 24 2007

Keywords

• nonn
• base

Links

• Seth A. Troisi, Table of n, a(n) for n = 2..100 (terms n=2..53 from Martin Renner)
• I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
• Index entries for sequences related to truncatable primes

Crossrefs

Cf. A024763, A024764, A024765, A024766, A024767, A024768, A024769, A024770, A076623.

Programs

Python

from sympy import isprime, primerange
from sympy.ntheory.digits import digits
def fromdigits(digs, base):
    return sum(d*base**i for i, d in enumerate(digs))
def a(n):
    prime_lists, an = [(p,) for p in primerange(1, n)], 0
    digits = 1
    while len(prime_lists) > 0:
        an += len(prime_lists)
        candidates = set((d,)+p for p in prime_lists for d in range(1, n))
        prime_lists = [c for c in candidates if isprime(fromdigits(c, n))]
        digits += 1
    return an
print([a(n) for n in range(2, 27)]) # Michael S. Branicky, May 03 2022