A088274 -id:A088274 - cp's OEIS frontend

A111022 Integers n such that 8*10^n+21 is prime.

0, 1, 2, 4, 10, 40, 55, 162, 264, 506, 870, 948, 1339, 3587, 6428, 48490, 81487

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "80021".

a(18) > 10^5. - Robert Price, Feb 06 2017

			n = 4 is a member because: 8*10^4+21 = 8*10000+21 = 80000+21 = 80021, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054, A110980.

a(15) from Ray Chandler, Dec 23 2010
Prepended a(1)=0 and a(2)=1 by Robert Price, Feb 06 2017
a(16)-a(17) from Robert Price, Feb 06 2017

A111023 Integers n such that 9*10^n + 11 is a prime number.

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 16, 20, 27, 115, 180, 274, 576, 1111, 2404, 5127, 8082, 9514, 12808, 14752, 15926, 22670, 37432, 41988, 53707, 72595, 92742

Offset: 1

Julien Peter Benney (jpbenney(AT)ftml.net), Oct 04 2005

See Kamada link - primecount.txt for terms, primesize.txt for discovery details including probable or proved primes - search on "90w11".

a(28) > 10^5. - Robert Price, Jan 28 2017

			n = 6 is a member because 9*10^6 + 11 = 9*1000000 + 11 = 9000011, which is prime.

Makoto Kamada, List of near-repdigit-related prime numbers.
Index entries for primes involving repunits.

Cf. A100275 = numbers n such that 9*10^n-11 is prime.

Cf. A049054, A088274, A088275, A095688, A107083, A108049, A108050, A108052, A108054, A110980.

Do[If[PrimeQ[9*10^n+11],Print[n]],{n,1,1300}] (* Zak Seidov, Sep 14 2006 *)

Edited by N. J. A. Sloane, Apr 11 2008
a(16)-a(22) from Ray Chandler, Dec 23 2010
a(23)-a(27) from Robert Price, Jan 28 2017

A356987 Primes whose decimal expansion is 1, zero or more 0's, then a single digit.

Original entry on oeis.org

11, 13, 17, 19, 101, 103, 107, 109, 1009, 10007, 10009, 100003, 1000003, 100000007, 1000000007, 1000000009, 100000000003, 100000000000000003, 1000000000000000003, 1000000000000000009, 10000000000000000000009, 1000000000000000000000007

Offset: 1

Marco Ripà, Sep 08 2022

The sequence is a subsequence of A139054.
All the terms of this sequence are of the form 10^k + m, where m belongs to the set {1, 3, 7, 9} and k is a nonnegative integer.
If a term is of the form 10^k+m and k is odd, then m > 1. - Chai Wah Wu, Oct 22 2022

			1000000007 is a term because it is a prime number whose decimal expansion is 1, 8 zeros, then the single digit 7.

Jonasz Aleszkiewicz, Algoritmika/primes.md.

Cf. A049054, A088274, A088275, A139054, A159031, A159352.

PrmsUpTo10PowNpl9[n_] := Parallelize @ Cases[ Table[10^k+m,{k,n},{m,{1,3,7,9}}], ?PrimeQ, {2}]; PrmsUpTo10PowNpl9[1000] (* _Mikk Heidemaa, Jan 07 2023 *)

from itertools import count, islice
from sympy import isprime
def A356987_gen(): # generator of terms
    return filter(isprime,(10**k+m for k in count(1) for m in (1,3,7,9)))
A356987_list = print(list(islice(A356987_gen(),30))) # Chai Wah Wu, Oct 22 2022

cp's OEIS Frontend

A111022 Integers n such that 8*10^n+21 is prime.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A111023 Integers n such that 9*10^n + 11 is a prime number.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Extensions

A356987 Primes whose decimal expansion is 1, zero or more 0's, then a single digit.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Python