A068817
Numbers k such that k concatenated with k 1's is a prime.
Original entry on oeis.org
1, 2, 5, 7, 10, 16, 20, 65, 91, 119, 169, 290, 428, 610, 905, 1051, 3488, 4526, 6445, 8693, 32059, 111860
Offset: 1
5 is a member as 5 followed by five 1's, 511111, is a prime.
- Jason Earls, On Smarandache Repunit N Numbers, Smarandache Notions Journal (2004), Vol. 14.1, pp. 251-258.
-
Do[ If[ PrimeQ[ FromDigits[ Join[IntegerDigits[n], IntegerDigits[(10^n - 1)/9]]]], Print[n]], {n, 1, 1700}]
-
for(n=1,520, if(isprime(n*10^n+(10^n-1)/9)==1,print1(n,",")))
a(18)-a(19) (probable primes) from
Jason Earls, Oct 15 2002
A261364
Semiprimes that are the concatenation of n 1's, 2^n and n 1's.
Original entry on oeis.org
121, 1118111, 1111161111, 11111164111111, 111111111512111111111, 1111111111114096111111111111, 111111111111181921111111111111, 111111111111111638411111111111111, 111111111111111111262144111111111111111111, 11111111111111111111104857611111111111111111111
Offset: 1
a(1) = 121 because the concatenation of 1, 2 and 1 is a semiprime number.
a(2) = 1118111 because the concatenation of 111, 8 and 111 is a semiprime number.
a(3) = 1111161111 because the concatenation of 1111, 16 and 1111 is a semiprime number.
-
ncat:= (a,b) -> 10^(1+ilog10(b))*a+b:
f:= proc(n) local N;
N:= ncat(ncat((10^n-1)/9,2^n),(10^n-1)/9);
if numtheory:-bigomega(N) = 2 then N else NULL fi
end proc:
seq(f(n),n=1..25); # Robert Israel, Oct 04 2015
-
Select[Table[FromDigits[Flatten[{PadRight[{},n,1],IntegerDigits[2^n],PadRight[{},n,1]}]],{n,20}], PrimeOmega[#]==2&] (* Harvey P. Dale, Dec 02 2023 *)
-
for(n=1, 25, if(bigomega(k=eval(Str((10^n - 1)/9, 2^n, (10^n - 1)/9))) == 2, print1(k", ")))
A262399
Primes that are the concatenation of n 1's, 2*n and n 1's.
Original entry on oeis.org
11411, 111181111, 111111011111, 111111111111112811111111111111
Offset: 1
a(1) = 11411 because the concatenation of 11, 4 and 11 is a prime number.
a(2) = 111181111 because the concatenation of 1111, 8 and 1111 is a prime number.
a(3) = 111111011111 because the concatenation of 11111, 10 and 11111 is a prime number.
-
Select[Table[w = Table[1, {k}]; FromDigits@ Join[w, IntegerDigits[2 k], w], {k, 60}], PrimeQ] (* Michael De Vlieger, Sep 21 2015 *)
Select[Table[FromDigits[Flatten[Join[{PadRight[{},n,1],IntegerDigits[2n],PadRight[{},n,1]}]]],{n,20}],PrimeQ] (* Harvey P. Dale, Feb 25 2024 *)
-
for(n=1, 1e3, if(isprime(k=eval(Str((10^n - 1)/9, 2*n, (10^n - 1)/9))), print1(k", ")))
-
use ntheory ":all"; for my $n (1..1e5) { my $s=join("", "1" x $n, 2*$n, "1" x $n); say $s if is_prob_prime($s); } # Dana Jacobsen, Oct 13 2015
A263299
Primes that are the concatenation of k 1's, the digits of k^2 + k + 1, and k 1's.
Original entry on oeis.org
131, 11113111, 1111211111, 111113111111, 11111143111111, 11111111111111111111111
Offset: 1
131 is in the list because 131 is a concatenation of 1, (1^2 + 1 + 1) = 3 and 1, and because 131 is prime.
-
Select[FromDigits/@Table[Join[PadRight[{},n,1],IntegerDigits[n^2+n+1],PadRight[{},n,1]],{n,20}],PrimeQ] (* Harvey P. Dale, Jan 27 2019 *)
-
for(n=1, 1e3, if(isprime(k=eval(Str((10^n - 1)/9, n^2 + n + 1, (10^n - 1)/9))), print1(k", ")))
-
from gmpy2 import is_prime
A263299_list = [n for n in (int('1'*k+str(k*(k+1)+1)+'1'*k) for k in range(10**2)) if is_prime(n)] # Chai Wah Wu, Oct 19 2015
Showing 1-4 of 4 results.
Comments