A068660 -id:A068660 - cp's OEIS frontend

A261618 Concatenation of n, n+1 and n.

121, 232, 343, 454, 565, 676, 787, 898, 9109, 101110, 111211, 121312, 131413, 141514, 151615, 161716, 171817, 181918, 192019, 202120, 212221, 222322, 232423, 242524, 252625, 262726, 272827, 282928, 293029, 303130, 313231, 323332, 333433, 343534, 353635, 363736

Offset: 1

José de Jesús Camacho Medina, Sep 09 2015

787, 9109, 111211, 131413, ... are primes. - N. J. A. Sloane, Sep 21 2015

			a(1) = concatenation(1, 2, 1) = 121.
a(10) = concatenation(10, 11, 10) = 101110.

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

Cf. A134810, A068660.

[Seqint(Intseq(n) cat Intseq(n+1) cat Intseq(n)):n in [1..36]]; // Marius A. Burtea, Dec 29 2019

f:= n -> n + 10^(1+ilog10(n))*(n+1)+10^(2+ilog10(n)+ilog10(n+1))*n:
map(f, [$1..100]); # Robert Israel, Dec 29 2019

Map[FromDigits@ Join[#1, #2, #1] & @@ IntegerDigits[#] &, Partition[Range@ 37, 2, 1]] (* Michael De Vlieger, Dec 29 2019 *)

a(n) = eval(concat(Str(n), concat(Str(n+1), Str(n)))); \\ Michel Marcus, Sep 10 2015

More terms from Michel Marcus, Sep 10 2015

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

A261618 Concatenation of n, n+1 and n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Magma

Maple

Mathematica

PARI

Extensions