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A264814
Numbers k such that concatenate(k,k+1,k) is prime.
1
7, 9, 11, 13, 33, 37, 39, 41, 47, 57, 59, 61, 69, 71, 77, 79, 81, 83, 101, 103, 129, 149, 181, 187, 189, 191, 193, 207, 217, 229, 231, 241, 289, 291, 299, 301, 303, 307, 317, 333, 347, 359, 373, 377, 383, 387, 409, 439, 451, 467, 473, 487, 489, 509, 517, 527
OFFSET
1,1
COMMENTS
Motivated by sequence A068660 which lists these primes.
LINKS
EXAMPLE
11 is in the sequence because 111211 is prime.
13 is in the sequence because 131413 is prime.
15 is not in the sequence because 151615 = 5 * 30323.
MATHEMATICA
Select[Range[800], PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[# + 1], IntegerDigits[#]]]] &] (* Alonso del Arte, Nov 25 2015 *)
PROG
(PARI) is(n)=isprime(eval(Str(n, n+1, n)))
(Magma) [n: n in [1..700] | IsPrime(Seqint(Intseq(n) cat Intseq(n+1) cat Intseq(n)))]; // Vincenzo Librandi, Nov 30 2015
(Python)
from sympy import isprime
def aupto(N):
return [k for k in range(1, N+1, 2) if isprime(int(str(k)+str(k+1)+str(k)))]
print(aupto(530)) # Michael S. Branicky, Jul 09 2021
CROSSREFS
KEYWORD
nonn,base
AUTHOR
M. F. Hasler, Nov 25 2015
STATUS
approved