A153332 Numbers k such that (10^k - 1)*150/99 + 1 is prime.

2, 14, 62, 88, 244, 582, 1790, 2122, 7232

Offset

1,1

Comments

These numbers are always even. If k is odd, then 10^k - 1 produces a number with an odd number of 9's which 99 does not divide. Also the numbers produced by this formula are palindromic.

Links

Table of n, a(n) for n=1..9.

Example

For the first entry, k=2, the formula produces the prime 151.

Mathematica

2*Floor[IntegerLength[#]/2]&/@Select[Table[FromDigits[Join[{1}, PadRight[ {}, 2n, {5, 1}]]], {n, 1000}], PrimeQ] (* Harvey P. Dale, Jun 27 2012 *)

Prog

(PARI) /* n=number of values to test, r=repeat digits, e.g., 14, 121, 177, 1234, etc.
d = last digit appended to the end */
repr(n, r, d) = ln=length(Str(r)); for(x=0, n, y=(10^(ln*x)-1)*10*r/(10^ln-1)+1; if(ispseudoprime(y), print1(ln*x", ")))
(Python)
from sympy import isprime
def afind(limit, startk=2):
    k = startk + (startk%2)
    t = int("1" + "51"*(k//2))
    for k in range(startk, limit+1, 2):
        if isprime(t): print(k, end=", ")
        t *= 100
        t += 51
afind(600) # Michael S. Branicky, Dec 13 2021

Crossrefs

Sequence in context: A174704 A058738 A095376 * A331822 A217154 A144657

Adjacent sequences: A153329 A153330 A153331 * A153333 A153334 A153335

Keyword

nonn,base,hard,more

Author

Cino Hilliard, Dec 23 2008

Extensions

a(7) provided by Harvey P. Dale, Jun 27 2012

Offset edited and a(8)-a(9) from Michael S. Branicky, Dec 13 2021

Status

approved