A285553 Numbers k such that (43*10^k - 403)/9 is prime.

1, 2, 3, 6, 11, 20, 23, 24, 26, 36, 56, 224, 411, 543, 611, 1541, 1632, 3719, 3888, 4917, 11454, 24275, 51816, 58563, 119024

Offset

1,2

Comments

For k > 1, numbers k such that the digit 4 followed by k-2 occurrences of the digit 7 followed by the digits 33 is prime (see Example section).

a(26) > 2*10^5.

Links

Table of n, a(n) for n=1..25.

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

Makoto Kamada, Search for 47w33.

Example

3 is in this sequence because (43*10^3 - 403)/9 = 4733 is prime.
Initial terms and associated primes:
a(1) = 1, 3;
a(2) = 2, 433;
a(3) = 3, 4733;
a(4) = 6, 4777733;
a(5) = 11, 477777777733; etc.

Maple

select(k->isprime((43*10^k-403)/9), [$1..1000]); # Muniru A Asiru, Jan 05 2019

Mathematica

Select[Range[1, 100000], PrimeQ[(43*10^# - 403)/9] &]

Crossrefs

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

Sequence in context: A018169 A238644 A191629 * A242842 A327665 A131269

Adjacent sequences: A285550 A285551 A285552 * A285554 A285555 A285556

Keyword

nonn,more,hard

Author

Robert Price, Apr 24 2017

Extensions

a(25) from Robert Price, Jan 04 2019

Status

approved