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

1,2

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

References

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

Links

Table of n, a(n) for n=1..22.

Example

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

Mathematica

Do[ If[ PrimeQ[ FromDigits[ Join[IntegerDigits[n], IntegerDigits[(10^n - 1)/9]]]], Print[n]], {n, 1, 1700}]
Select[Range[5000], PrimeQ[FromDigits[Join[IntegerDigits[#], PadRight[{}, #, 1]]]]&] (* The program generates the first 18 terms of the sequence. *) (* Harvey P. Dale, Sep 15 2025 *)

Prog

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

Crossrefs

Cf. A070220, A070746.

Sequence in context: A172410 A266594 A103871 * A156779 A345127 A226813

Adjacent sequences: A068814 A068815 A068816 * A068818 A068819 A068820

Keyword

nonn,base,more

Author

Amarnath Murthy, Mar 07 2002

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

Status

approved