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

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

Offset: 1

Author

Marco Ripà, Sep 08 2022

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Jonasz Aleszkiewicz, Algoritmika/primes.md.

Crossrefs

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

Programs

Mathematica

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

Python

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