A264814 Numbers k such that concatenate(k,k+1,k) is prime.

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

Michael S. Branicky, Table of n, a(n) for n = 1..10000

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

Cf. A068659, A068660, A262205.

Sequence in context: A055741 A103621 A081239 * A029612 A120165 A267970

Adjacent sequences: A264811 A264812 A264813 * A264815 A264816 A264817

Keyword

nonn,base

Author

M. F. Hasler, Nov 25 2015

Status

approved