A092993
Smallest prime of the form concatenation(s) of prime(n) with itself followed by a 3, or 0 if no such prime exists.
Original entry on oeis.org
23, 0, 53, 73, 113, 13131313133, 173, 193, 233, 293, 313, 373, 41413, 433, 47474747474747474747474747473, 53535353535353535353535353533, 593, 613, 673, 71713, 733, 0, 83833, 89898989893, 97973, 1013, 1033, 1071071071073, 1093
Offset: 1
For a(1), start with prime(1)=2. Since appending a digit 3 yields the prime 23, a(1)=23.
For a(2), start with prime(2)=3. Since concatenating any number of digits '3' never yields a prime, a(2)=0.
For a(6), starting with prime(6)=13, one has to take 5 concatenations of itself before a prime is obtained when a final digit '3' is appended, thus a(6)=13131313133.
a(22)=0 since the concatenation of prime(22)=79 with itself, followed by a 3, is always composite. - _Giovanni Resta_, Apr 07 2006
A092992
Smallest prime of the form concatenation of prime(n) with itself followed by a 1.
Original entry on oeis.org
2221, 31, 555555555551, 71, 1111111111111111111, 131, 1717171717171717171717171717171, 191, 2323231, 29292929291, 311, 3737373737373737373737371, 41411, 431
Offset: 1
A092995
Smallest prime of the form concatenation of prime(n) with itself followed by a 9, or 0 if no such prime exists.
Original entry on oeis.org
29, 0, 59, 79, 11119, 139, 179, 199, 239, 29292929292929299, 31319, 379, 419, 439, 479, 0, 599, 619, 67679, 719, 739, 797979799, 839, 89899, 979797979, 1019, 1039, 1071071071079, 1091091091099, 1131139, 1279, 1319, 1371371371379, 1399, 1499
Offset: 1
A210513
Primes formed by concatenating k, k, and 7.
Original entry on oeis.org
227, 337, 557, 887, 997, 11117, 24247, 26267, 27277, 29297, 30307, 32327, 39397, 48487, 51517, 54547, 60607, 62627, 65657, 68687, 69697, 72727, 74747, 78787, 81817, 87877, 89897, 90907, 92927, 93937, 95957, 101710177, 101910197, 103110317, 103410347, 103810387
Offset: 1
For k = 2, a(1) = 227.
For k = 3, a(2) = 337.
For k = 5, a(3) = 557.
For k = 8, a(4) = 887.
For k = 9, a(5) = 997.
-
Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], {7}}]], {n, 100}], PrimeQ] (* Alonso del Arte, Feb 01 2013 *)
-
import numpy as np
from functools import reduce
def factors(n):
return reduce(list._add_, ([i, n//i] for i in range(1, int(n**0.5) + 1) if n % i == 0))
for i in range(1, 2000):
p1=int(str(i)+str(i)+"7")
if len(factors(p1))<3:
print(p1, end=',')
-
from sympy import isprime
from itertools import count, islice
def agen(): yield from filter(isprime, (int(str(k)+str(k)+'7') for k in count(1)))
print(list(islice(agen(), 36))) # Michael S. Branicky, Jul 26 2022
Showing 1-4 of 4 results.
Comments