A273679 Numbers k such that 10^k - 1000000001 is prime.

11, 18, 22, 26, 27, 36, 45, 59, 140, 162, 201, 278, 427, 563, 588, 757, 951, 2006, 3938, 4127, 4490, 5637, 6074, 6725, 7025, 10191, 25628, 39415, 51872, 57501, 90227, 115773, 117142, 148934

Offset

1,1

Comments

For k > 9, numbers k such that k-10 occurrences of the digit 9 followed by the digits 8999999999 is prime (see Example section).

a(35) > 2*10^5.

Links

Table of n, a(n) for n=1..34.

Makoto Kamada, Factorization of near-repdigit-related numbers.

Makoto Kamada, Search for 9w8999999999.

Example

11 is in this sequence because 10^11 - 1000000001 = 98999999999 is prime.
Initial terms and associated primes:
a(1) = 11, 98999999999,
a(2) = 18, 999999998999999999,
a(3) = 22, 9999999999998999999999,
a(4) = 26, 99999999999999998999999999,
a(5) = 27, 999999999999999998999999999, etc.

Mathematica

Select[Range[0, 100000], PrimeQ[10^#-1000000001] &]

Prog

(PARI) is(n)=ispseudoprime(10^n-10^9-1) \\ Charles R Greathouse IV, Jun 08 2016
(Python)
from sympy import isprime
def afind(limit):
    tenk = 10**10
    for k in range(10, limit+1):
        if isprime(tenk - 1000000001): print(k, end=", ")
        tenk *= 10
afind(100000) # Michael S. Branicky, Nov 18 2021

Crossrefs

Cf. A056654, A268448, A269303, A270339, A270613, A270831, A270890, A270929, A271269.

Sequence in context: A242918 A287868 A095648 * A250192 A250217 A335278

Adjacent sequences: A273676 A273677 A273678 * A273680 A273681 A273682

Keyword

nonn,more

Author

Robert Price, May 27 2016

Extensions

a(32)-a(33) from Robert Price, Mar 01 2018

a(34) from Robert Price, Dec 31 2020

Status

approved