|
| |
|
|
A085733
|
|
Right-truncatable semiprimes.
|
|
6
|
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
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
|
| |
|
|
