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A210513
Primes formed by concatenating k, k, and 7.
2
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
1,1
COMMENTS
This sequence is similar to A030458, A052089, and A092994.
Base considered is 10.
Observations:
- k cannot be a multiple of 7.
- k cannot have a digital root 7 as the sum of the digits would be divisible by 3.
- There is no k between 100 and 1000 that can form a prime number of this form after 95957 the next prime is 101710177.
- k cannot have a digital root equal to 1 or 4, because then in the concatenation it contributes 2 or 8 to the digital root of the number, and that number is then divisible by 3.
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Table[FromDigits[Flatten[{IntegerDigits[n], IntegerDigits[n], {7}}]], {n, 100}], PrimeQ] (* Alonso del Arte, Feb 01 2013 *)
PROG
(Python)
from sympy import isprime
for i in range(1, 1100):
p1=int(str(i)+str(i)+"7")
if isprime(p1):
print(p1, end=', ')
(Python)
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
CROSSREFS
KEYWORD
base,nonn,easy
AUTHOR
Abhiram R Devesh, Jan 26 2013
EXTENSIONS
a(34) and beyond from Michael S. Branicky, Jul 26 2022
STATUS
approved