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

2,3

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

Table of n, a(n) for n=2..48.

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

Prog

(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

Crossrefs

Cf. A076586.

Sequence in context: A012611 A356109 A356175 * A246164 A124183 A218643

Adjacent sequences: A133754 A133755 A133756 * A133758 A133759 A133760

Keyword

nonn

Author

Martin Renner, Jan 04 2008

Extensions

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

Status

approved