A085733 Right-truncatable semiprimes.

4, 6, 9, 46, 49, 62, 65, 69, 91, 93, 94, 95, 466, 469, 493, 497, 622, 623, 626, 629, 655, 694, 695, 697, 698, 699, 913, 914, 917, 933, 934, 939, 943, 949, 951, 955, 958, 959, 4661, 4666, 4667, 4694, 4699, 4934, 4939, 4971, 4979, 6227, 6233, 6238

Offset

1,1

Comments

Semiprimes in which repeatedly deleting the rightmost digit gives a semiprime at every step until a single-digit semiprime remains.

The sequence is finite. According to Shyam Sunder Gupta the number 95861957783594714393831931415189937897 is the largest right-truncatable semiprime.

The total number of right-truncatable semiprimes including the single-digit semiprimes 4, 6 and 9 is 56076. - Shyam Sunder Gupta, Jan 13 2008

No term ends in (or contains) 0 else it would be divisible by 2, 5, and some other factor. - Michael S. Branicky, Aug 04 2022

References

Shyam Sunder Gupta, Truncatable semi-primes, Mathematical Spectrum 39:3 (2007), pp. 109-112.

Links

Michael S. Branicky, Table of n, a(n) for n = 1..56076 (full sequence).

I. O. Angell and H. J. Godwin, On truncatable primes, Math. Comput. 31:137, 265-267, 1977.

G. L. Honaker, Jr., Prime Curios! 46613113151331733179

Shyam Sunder Gupta, The largest right-truncatable semiprime. Prime Curios.

Index entries for sequences related to truncatable primes

Prog

(Python)
from sympy import factorint
from itertools import islice
def issemiprime(n): return sum(factorint(n).values()) == 2
def agen():
    semis, digits = [4, 6, 9], "123456789" # can't end in 0
    while len(semis) > 0:
        yield from semis
        cands = set(int(str(p)+d) for p in semis for d in digits)
        semis = sorted(c for c in cands if issemiprime(c))
print(list(islice(agen(), 50))) # Michael S. Branicky, Aug 04 2022

Crossrefs

Cf. A001358, A213019, A086697.

Sequence in context: A175459 A257652 A107665 * A242751 A107342 A086698

Adjacent sequences: A085730 A085731 A085732 * A085734 A085735 A085736

Keyword

nonn,base,fini,full

Author

G. L. Honaker, Jr., Jul 20 2003

Extensions

More terms from Reinhard Zumkeller, Jul 22 2003

More terms from Hugo Pfoertner, Jul 22 2003

Status

approved