A139054 -id:A139054 - cp's OEIS frontend

A139053 Array read by rows: row n lists the first 3 primes with n digits.

2, 3, 5, 11, 13, 17, 101, 103, 107, 1009, 1013, 1019, 10007, 10009, 10037, 100003, 100019, 100043, 1000003, 1000033, 1000037, 10000019, 10000079, 10000103, 100000007, 100000037, 100000039, 1000000007, 1000000009, 1000000021, 10000000019, 10000000033, 10000000061

Offset: 1

Omar E. Pol, Apr 08 2008

Michael S. Branicky, Table of n, a(n) for n = 1..3000

Cf. A000040, A003617, A073914, A139052, A139054.

np[n_]:=Module[{a=NextPrime[10^n]},{a,NextPrime[a], NextPrime[NextPrime[ a]]}]; Flatten[Array[np,12,0]] (* Harvey P. Dale, Dec 14 2011 *)
Flatten@Array[NextPrime[10^#,{1,2,3}]&,12,0] (* Giorgos Kalogeropoulos, May 06 2019 *)

from sympy import nextprime
def auptodigs(maxdigits):
  alst = []
  for n in range(1, maxdigits+1):
    p1 = nextprime(10**(n-1))
    p2 = nextprime(p1)
    p3 = nextprime(p2)
    alst.extend([p1, p2, p3])
  return alst
print(auptodigs(11)) # Michael S. Branicky, May 07 2021

More terms from Max Alekseyev, Dec 12 2011

a(32) and beyond from Michael S. Branicky, May 07 2021

A139052 Array read by rows: row n lists the first two primes with n digits.

Original entry on oeis.org

2, 3, 11, 13, 101, 103, 1009, 1013, 10007, 10009, 100003, 100019, 1000003, 1000033, 10000019, 10000079, 100000007, 100000037, 1000000007, 1000000009, 10000000019, 10000000033, 100000000003, 100000000019, 1000000000039, 1000000000061

Offset: 1

Omar E. Pol, Apr 08 2008

Cf. A000040, A003617, A073914, A139053, A139054.

ftp[d_]:=Module[{np1=NextPrime[10^(d-1)]},{np1,NextPrime[np1]}]; Array[ ftp,15]//Flatten (* Harvey P. Dale, Mar 27 2021 *)

More terms from Sean A. Irvine, Jun 02 2011

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

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A139053 Array read by rows: row n lists the first 3 primes with n digits.

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A139052 Array read by rows: row n lists the first two primes with n digits.

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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

Python