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
Examples
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.
Links
- Michael S. Branicky, Table of n, a(n) for n = 1..10000
Programs
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Magma
[n: n in [1..700] | IsPrime(Seqint(Intseq(n) cat Intseq(n+1) cat Intseq(n)))]; // Vincenzo Librandi, Nov 30 2015
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Mathematica
Select[Range[800], PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[# + 1], IntegerDigits[#]]]] &] (* Alonso del Arte, Nov 25 2015 *)
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PARI
is(n)=isprime(eval(Str(n,n+1,n)))
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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
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