A278397 - OEIS

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A278397

Numbers k such that 10^k - 20001 is prime.

1

5, 11, 16, 21, 37, 83, 94, 299, 318, 467, 622, 707, 1931, 2175, 2189, 2238, 2526, 5202, 10541, 15822, 17407, 19919, 19998, 25407, 96377, 118009

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OFFSET

1,1

COMMENTS

For k > 4, numbers k such that k-5 occurrences of the digit 9 followed by the digits 79999 is prime (see Example section).

a(27) > 2*10^5.

LINKS

Table of n, a(n) for n=1..26.

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

Makoto Kamada, Search for 9w79999.

EXAMPLE

5 is in this sequence because 10^5 - 20001 = 79999 is prime.

Initial terms and associated primes:

a(1) = 5, 79999;

a(2) = 11, 99999979999;

a(3) = 16, 9999999999979999;

a(4) = 21, 999999999999999979999;

a(5) = 37, 9999999999999999999999999999999979999; etc.

MATHEMATICA

Select[Range[0, 100000], PrimeQ[10^# - 20001] &]

PROG

(Magma) [n: n in [5..400] | IsPrime(10^n - 20001)]; // Vincenzo Librandi, Nov 21 2016

(PARI) is(n)=ispseudoprime(10^n-20001) \\ Charles R Greathouse IV, Jun 13 2017

CROSSREFS

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

Sequence in context: A314137 A314138 A314139 * A314140 A314141 A314142

Adjacent sequences: A278394 A278395 A278396 * A278398 A278399 A278400

KEYWORD

nonn,more,hard

AUTHOR

Robert Price, Nov 20 2016

EXTENSIONS

a(26) from Robert Price, Jan 26 2018

STATUS

approved