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A276672 Numbers n such that (19*10^n + 101) / 3 is prime. 0
1, 3, 4, 9, 10, 12, 13, 16, 20, 37, 57, 66, 106, 116, 127, 355, 396, 547, 2289, 3777, 4500, 7821, 15663, 22746, 25978, 30434, 39682 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For n>1, numbers such that the digit 6 followed by n-2 occurrences of the digit 3 followed by the digits 67 is prime (see Example section).

a(28) > 10^5.

LINKS

Table of n, a(n) for n=1..27.

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

Makoto Kamada, Search for 63w67.

EXAMPLE

3 is in this sequence because (19*10^3 + 101) / 3 = 6367 is prime.

Initial terms and primes associated:

a(1) = 1, 97;

a(2) = 3, 6367;

a(3) = 4, 63367;

a(4) = 9, 6333333367;

a(5) = 10, 63333333367, etc.

MATHEMATICA

Select[Range[0, 100000], PrimeQ[(19*10^# + 101) / 3] &]

PROG

(MAGMA) [n: n in [0..400] |IsPrime((19*10^n+101) div 3)]; // Vincenzo Librandi, Sep 13 2016

(PARI) is(n)=ispseudoprime((19*10^n+101)/3) \\ Charles R Greathouse IV, Jun 13 2017

CROSSREFS

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

Sequence in context: A010376 A010388 A283973 * A010400 A010439 A005836

Adjacent sequences:  A276669 A276670 A276671 * A276673 A276674 A276675

KEYWORD

nonn,more

AUTHOR

Robert Price, Sep 12 2016

STATUS

approved

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Last modified October 15 19:24 EDT 2018. Contains 316237 sequences. (Running on oeis4.)