A133757 Total number of restricted right truncatable primes in base n.

0, 1, 2, 4, 11, 7, 20, 23, 27, 28, 61, 61, 153, 130, 151, 157, 301, 343, 561, 806, 1046, 615, 1227, 2136, 2472, 2288, 3685, 2110, 5241, 4798, 7017, 10630, 14175, 14127, 21267, 15034, 24677, 29289, 46814, 29291, 63872, 58451, 82839, 143678, 196033, 99103, 218108

Offset: 2

Author

Martin Renner, Jan 04 2008

Keywords

• nonn

Comments

Prime digits p in base n are counted if there is no prime with 2 digits which can have its rightmost digit removed to produce p.

Links

• I. O. Angell and H. J. Godwin, On Truncatable Primes, Math. Comput. 31, 265-267, 1977.
• Eric Weisstein's World of Mathematics, Truncatable Prime.
• Index entries for sequences related to truncatable primes

Crossrefs

Cf. A076586.

Programs

Python

from sympy import isprime, primerange
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:
        new_prime_strs = set()
        for p in prime_lists:
            can_extend = False
            for d in range(n):
                c = (d, ) + p
                if isprime(fromdigits(c, n)):
                    can_extend = True
                    new_prime_strs.add(c)
            if not can_extend:
                an += 1
        prime_lists = list(new_prime_strs)
        digits += 1
    return an
print([a(n) for n in range(2, 27)]) # Michael S. Branicky, Dec 11 2022

Extensions

a(6) corrected and a(11) and beyond from Michael S. Branicky, Dec 11 2022