A068659 -id:A068659 - cp's OEIS frontend

A068660 Primes formed from the concatenation of k, k+1 and k for some k.

787, 9109, 111211, 131413, 333433, 373837, 394039, 414241, 474847, 575857, 596059, 616261, 697069, 717271, 777877, 798079, 818281, 838483, 101102101, 103104103, 129130129, 149150149, 181182181, 187188187, 189190189, 191192191, 193194193, 207208207, 217218217

Offset: 1

Amarnath Murthy, Mar 01 2002

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

Cf. A068659, A262205.

These are the primes in A261618. - M. F. Hasler, Nov 25 2015

[m: n in [2..300] | IsPrime(m) where m is Seqint(Intseq(n) cat Intseq(n+1) cat Intseq(n))]; // Vincenzo Librandi, Sep 28 2015

ncat:= (a,b) -> a*10^(1+ilog10(b))+b:
select(isprime, [seq(ncat(n,ncat(n+1,n)),n=1..1000,2)]); # Robert Israel, Oct 23 2015

concat[n_]:=Module[{idn=IntegerDigits[n]},FromDigits[Join[idn, IntegerDigits[ n+1],idn]]]; Select[concat/@Range[200],PrimeQ] (* Harvey P. Dale, Aug 20 2014 *)
A = Table[(n*10^(Floor[Log[10, 10(n+1)]])+(n+1))*10^(Floor[Log[10, 10(n)]])+n, {n, 1, 120}]; Select[A, PrimeQ] (* José de Jesús Camacho Medina, Sep 09 2015 *)
Select[Table[FromDigits[Join[Flatten[IntegerDigits[{n, n + 1, n}]]]], {n, 200}], PrimeQ] (* Vincenzo Librandi, Sep 28 2015 *)

for(n=1, 1e3, if(isprime(k=eval(Str(n, n+1, n))), print1(k", "))) \\ Altug Alkan, Sep 28 2015

from sympy import isprime
def aupto(N):
  return [t for t in (int(str(k)+str(k+1)+str(k)) for k in range(1, N+1, 2)) if isprime(t)]
print(aupto(217)) # Michael S. Branicky, Jul 09 2021

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

Original entry on oeis.org

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

M. F. Hasler, Nov 25 2015

Motivated by sequence A068660 which lists these primes.

			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.

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

Cf. A068659, A068660, A262205.

[n: n in [1..700] | IsPrime(Seqint(Intseq(n) cat Intseq(n+1) cat Intseq(n)))]; // Vincenzo Librandi, Nov 30 2015

Select[Range[800], PrimeQ[FromDigits[Join[IntegerDigits[#], IntegerDigits[# + 1], IntegerDigits[#]]]] &] (* Alonso del Arte, Nov 25 2015 *)

PARI
```
is(n)=isprime(eval(Str(n,n+1,n)))
```

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

cp's OEIS Frontend

A068660 Primes formed from the concatenation of k, k+1 and k for some k.

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