A068817 Numbers k such that k concatenated with k 1's is a prime.

1, 2, 5, 7, 10, 16, 20, 65, 91, 119, 169, 290, 428, 610, 905, 1051, 3488, 4526, 6445, 8693, 32059, 111860

Offset: 1

Author

Amarnath Murthy, Mar 07 2002

Keywords

• nonn
• base
• more

Comments

There is no further term up to 10000. - Farideh Firoozbakht, Sep 23 2009

No more terms through 20000. - Jon E. Schoenfield, Mar 24 2018

a(22) > 50000, if it exists. - Giovanni Resta, Jun 28 2018

Examples

			5 is a member as 5 followed by five 1's, 511111, is a prime.
		

References

• Jason Earls, On Smarandache Repunit N Numbers, Smarandache Notions Journal (2004), Vol. 14.1, pp. 251-258.

Crossrefs

Cf. A070220, A070746.

Programs

Mathematica

Do[ If[ PrimeQ[ FromDigits[ Join[IntegerDigits[n], IntegerDigits[(10^n - 1)/9]]]], Print[n]], {n, 1, 1700}]

PARI

for(n=1,520, if(isprime(n*10^n+(10^n-1)/9)==1,print1(n,",")))

Extensions

More terms from Benoit Cloitre, Mar 09 2002

Further terms from Vladeta Jovovic, Amarnath Murthy and Robert G. Wilson v, May 03 2002

a(17) (a probable prime) from Rick L. Shepherd, May 10 2002

a(18)-a(19) (probable primes) from Jason Earls, Oct 15 2002

a(20) from Farideh Firoozbakht, Sep 23 2009

a(21) from Giovanni Resta, Jun 28 2018

a(22) from Michael S. Branicky, Jun 30 2025