A153331 Numbers k such that (10^k - 1)*140/99 + 1 is prime.

10, 276, 478, 582, 1630, 6342, 14688

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 these numbers are palindromic.

a(8) > 50000. - Michael S. Branicky, Jan 15 2026

Links

Table of n, a(n) for n=1..7.

Example

10 is a term, because (10^10 - 1)*140/99 + 1 = 14141414141 is prime.

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", ")))
repr(10^3, 14, 1)
(Python)
from sympy import isprime
def afind(limit, startk=2):
    k = startk + (startk%2)
    t = int("1" + "41"*(k//2))
    for k in range(startk, limit+1, 2):
        if isprime(t): print(k, end=", ")
        t *= 100
        t += 41
afind(600) # Michael S. Branicky, Dec 13 2021

Crossrefs

Sequence in context: A222998 A368770 A221526 * A290202 A203149 A117654

Adjacent sequences: A153328 A153329 A153330 * A153332 A153333 A153334

Keyword

nonn,base,hard,more

Author

Cino Hilliard, Dec 23 2008

Extensions

a(6) from Michael S. Branicky, Dec 13 2021

a(7) from Michael S. Branicky, May 14 2023

Status

approved