Timothy Smith has authored 2 sequences.
A347864
Left- or right-truncatable primes, restricted to one consecutive zero.
Original entry on oeis.org
2, 3, 5, 7, 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97, 103, 107, 113, 131, 137, 139, 167, 173, 179, 197, 223, 229, 233, 239, 271, 283, 293, 307, 311, 313, 317, 331, 337, 347, 353, 359, 367, 373, 379, 383, 397, 431, 433, 439, 443, 467, 479, 503
Offset: 1
Left- or right-truncatable primes, excluding all 0s:
A137812.
The number of primes of length n following these rules:
A346662.
-
from sympy import isprime
route = set({})
nums = [i*(10**j) for i in range(1, 10) for j in range(2)]
def addnum(a):
global route
for j in nums:
b = int("{}{}".format(a, j))
if isprime(b):
if b not in route:
route.add(b)
addnum(b)
for j in nums:
b = int("{}{}".format(j, a))
if isprime(b):
if b not in route:
route.add(b)
addnum(b)
def run():
for i in nums:
if isprime(i):
addnum(i)
A346662
Number of n-digit left- or right-truncatable primes with no consecutive zero digits.
Original entry on oeis.org
4, 16, 76, 300, 955, 2648, 6402, 14339, 28684, 53450, 91284, 147064, 221301, 319067, 433227, 567565, 700765, 834464, 947055, 1050886, 1114368, 1157526, 1150645, 1117265, 1044757, 963722, 855804, 753172, 633786, 528122, 426328, 339866, 264078, 202013, 150330, 111055, 78996, 56123, 38874, 26644, 17944, 11898, 7878, 4945, 3255, 2024, 1323, 764, 464, 286, 158, 77, 40, 26, 14, 5, 5, 4, 1, 1
Offset: 1
The 16 two-digit left- or right-truncatable primes with no consecutive zero digits are 13, 17, 23, 29, 31, 37, 43, 47, 53, 59, 67, 71, 73, 79, 83, 97.
The first 10 three-digit left- or right-truncatable primes with no consecutive zero digits are 103, 107, 113, 131, 137, 139, 167, 173, 179, 197.
The unique 60-digit left- or right-truncatable prime with no consecutive zero digits can be sequentially truncated to a single-digit prime as follows, where each "..." indicates repeated removal of the leftmost digit:
202075909708030901050930450609080660821035604908735717137397
...
2075909708030901050930450609080660821035604908735717137397
207590970803090105093045060908066082103560490873571713739
...
970803090105093045060908066082103560490873571713739
97080309010509304506090806608210356049087357171373
...
6090806608210356049087357171373
609080660821035604908735717137
...
80660821035604908735717137
8066082103560490873571713
806608210356049087357171
...
8210356049087357171
821035604908735717
21035604908735717
2103560490873571
...
71
7
Left- or right-truncatable primes, excluding all 0s:
A137812.
Left- or right-truncatable primes with 0s allowed, but none consecutive:
A347864.
-
from sympy import isprime
dumps = set({})
route = set({})
nums = [i*(10**j) for i in range(1, 10) for j in range(2)]
def addnum(a):
global route
for j in nums:
b = int("{}{}".format(a, j))
if isprime(b):
if b not in route:
route.add(b)
addnum(b)
for j in nums:
b = int("{}{}".format(j, a))
if isprime(b):
if b not in route:
route.add(b)
addnum(b)
def run():
for i in nums:
if isprime(i):
addnum(i)
run()
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