A088275 -id:A088275 - cp's OEIS frontend

A110995 Integers k such that 6*10^k + 41 is a prime number.

0, 1, 2, 4, 6, 8, 50, 54, 102, 134, 212, 872, 3055, 3427, 3528, 4262, 4414, 6084, 93792

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 "60041".

a(20) > 10^5. - Robert Price, Jan 19 2017

			k = 4 is a term because 6*10^4 + 41 = 6*10000 + 41 = 60000 + 41 = 60041, which is a prime number.

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.

a(18) from Ray Chandler, Dec 23 2010
a(1)-a(2) prepended by Robert Price, Jan 19 2017
a(19) from Robert Price, Jan 19 2017

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

Original entry on oeis.org

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

A280828 Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

Original entry on oeis.org

4, 22, 202

Offset: 1

Sergey Pavlov, Jan 08 2017

Let k=2*10^(n-1)+2, then a(n)=10^k+9. For all k>4, k is a term of A058441.
The only known terms from A088275 (Numbers n such that 10^n + 9 is prime) that are of the form 2*10^j + 2 are 4, 22, and 202; given the lower bound given for that sequence's next term, a(4) >= 200002. - Jon E. Schoenfield, Jan 11 2017
For n<4, let k=a(n) and p=(10^k-9)/10^(k/2)+3=10^(k/2)+3, then p is prime. - Sergey Pavlov, Jan 13 2017

			For n=1, a(1)=4 and 10^4 + 9 is prime.

Cf. A043037, A058441, A088275, A144249, A205529.

Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

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

A359630 Primes p such that 10^p+3 or 10^p+9 is also prime.

Original entry on oeis.org

2, 3, 5, 11, 17, 101, 107, 26927, 48109

Offset: 1

Mikk Heidemaa, Jan 08 2023

Union of the terms which are prime in A049054 and in A088275.

If it exists, a(10) > 2*10^5 (according to the comment at A088275).

			3 is a term since it is prime and so is 10^3 + 9 = 1009.
11 is a term since it is prime and 10^11 + 3 = 100000000003 is also a prime.

Cf. A049054, A088275.

Block[{p}, ParallelDo[p := Prime @ i; If[(PrimeQ[10^p + 3] || PrimeQ[10^p + 9]), Print @ p], {i, PrimePi @ 48109}, Method -> "FinestGrained"]]
Select[Prime[Range[5000]],AnyTrue[10^#+{3,9},PrimeQ]&] (* Harvey P. Dale, Feb 09 2025 *)

cp's OEIS Frontend

A110995 Integers k such that 6*10^k + 41 is a prime number.

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

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

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A280828 Numbers k of the form 2*10^m + 2 such that 10^k + 9 is prime.

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

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Mathematica

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A359630 Primes p such that 10^p+3 or 10^p+9 is also prime.

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Mathematica