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A153331 Numbers k such that (10^k - 1)*140/99 + 1 is prime. 0
10, 276, 478, 582, 1630, 6342 (list; graph; refs; listen; history; text; internal format)
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. a(10) = 14141414141 which is prime. Also these numbers are palindromic.

LINKS

Table of n, a(n) for n=1..6.

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" + "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: A055055 A222998 A221526 * A290202 A203149 A117654

Adjacent sequences:  A153328 A153329 A153330 * A153332 A153333 A153334

KEYWORD

nonn,base,more

AUTHOR

Cino Hilliard, Dec 23 2008

EXTENSIONS

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

STATUS

approved

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Last modified January 16 04:59 EST 2022. Contains 350374 sequences. (Running on oeis4.)