A174352 -id:A174352 - cp's OEIS frontend

A145851 Primes of the form k followed by k 9's.

19, 49999, 599999, 1799999999999999999, 2099999999999999999999, 289999999999999999999999999999

Offset: 1

Lekraj Beedassy, Oct 21 2008

Corresponding k, which cannot be multiples of 3, are in A174352. The next term has 176 digits, too large to include here. - Rick L. Shepherd, Mar 22 2010

Cf. A141311, A145852.

Cf. A174352. - Rick L. Shepherd, Mar 22 2010

Select[Table[FromDigits[PadRight[{k},k+1,9]],{k,200}],PrimeQ] (* Harvey P. Dale, Jun 22 2022 *)

lista(nn) = for(k=1, nn, if(ispseudoprime(q=k*10^(k-1)-1), print1(q, ", "))); \\ Jinyuan Wang, Mar 24 2020

a(2) was 4999; corrected by Rick L. Shepherd, Mar 22 2010

A176091 Numbers n such that (10^n-1) * 10^ceiling(log_10(n+1)) + n is prime.

Original entry on oeis.org

307, 1759, 2963, 3881

Offset: 1

Rick L. Shepherd, Apr 16 2010

No term is a multiple of 2, 3, or 5. (In fact, a(1) through a(4) are prime.) The decimal expansion of each corresponding prime is n 9's with n's decimal expansion concatenated. Probable primes found by PrimeForm. Primes for 307 and 1759 proved by Primo. No more terms up to 30000.

Cf. A174352 (n followed by n 9's is prime), n k's followed by n is prime: A070746 (k=1), A176087 (k=3), A176089 (k=4), A176090 (k=6), A084428 (k=7). [k=2, 5, and 8 produce only composites divisible by 3.]

A174710 Numbers k such that k*10^k + (10^k - 1)/3 is prime.

Original entry on oeis.org

1, 2, 275, 1556, 36682

Offset: 1

Rick L. Shepherd, Mar 27 2010

No term is a multiple of 3. The decimal expansion of each corresponding prime is n's decimal expansion with n 3's concatenated. Primes and probable primes found by PrimeForm. Primes for 275 and 1556 proved by Primo. No more terms up to 30000.

No more terms up to 50000. - Michael S. Branicky, Oct 11 2024

			The numbers 1 and 2 are terms because 13 and 233 are prime.

Cf. A068817 (n followed by n 1's is prime), A133127 (n followed by n 7's is prime), A174352 (n followed by n 9's is prime).

is(n)=ispseudoprime(n*10^n+(10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(5) from Michael S. Branicky, Oct 11 2024

cp's OEIS Frontend

A145851 Primes of the form k followed by k 9's.

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A176091 Numbers n such that (10^n-1) * 10^ceiling(log_10(n+1)) + n is prime.

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A174710 Numbers k such that k*10^k + (10^k - 1)/3 is prime.

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