A261618 -id:A261618 - 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

A330699 Primes p such that the base-10 concatenation p||(p+1)||p is prime.

Original entry on oeis.org

7, 11, 13, 37, 41, 47, 59, 61, 71, 79, 83, 101, 103, 149, 181, 191, 193, 229, 241, 307, 317, 347, 359, 373, 383, 409, 439, 467, 487, 509, 569, 691, 823, 839, 857, 907, 941, 1061, 1069, 1091, 1109, 1123, 1181, 1193, 1303, 1423, 1447, 1487, 1499, 1579, 1601, 1697, 1777, 1831, 1871, 1931, 1949, 1979

Offset: 1

Robert Israel, Dec 26 2019

			a(3)=13 is a member because 13 and 131413 are primes.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A261618, A309935.

f:= proc(n) local d; d:=10^(ilog10(n)+1);
   n*(d^2+d+1)+d
end proc:
select(t -> isprime(t) and isprime(f(t)), [seq(i,i=3..10000,2)]);

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

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