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

Author

Robert Price, May 27 2016

Keywords

• nonn
• more

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.

Examples

			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.
		

Links

• Makoto Kamada, Factorization of near-repdigit-related numbers.
• Makoto Kamada, Search for 9w8999999999.

Crossrefs

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

Programs

Mathematica

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

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

Extensions

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

a(34) from Robert Price, Dec 31 2020