A293759 Numbers k such that (35*10^k - 197)/9 is prime.

1, 2, 4, 7, 8, 19, 26, 28, 38, 43, 67, 331, 359, 832, 907, 1880, 2359, 4301, 5896, 6187, 37154, 40411, 59584

Offset

1,2

Comments

For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 8 followed by the digits 67 is prime (see Example section).

a(24) > 2*10^5.

Links

Table of n, a(n) for n=1..23.

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

Makoto Kamada, Search for 38w67

Example

2 is in this sequence because (35*10^2 - 197)/9 = 367 is prime.
Initial terms and primes associated:
a(1) = 1, 17;
a(2) = 2, 367;
a(3) = 4, 38867;
a(4) = 7, 38888867;
a(5) = 8, 388888867; etc.

Mathematica

Select[Range[1, 100000], PrimeQ[(35*10^# - 197)/9] &]

Prog

(Magma) [n: n in [1..400] |IsPrime((35*10^n - 197) div 9)]; // Vincenzo Librandi, Oct 16 2017

Crossrefs

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

Sequence in context: A045594 A013056 A013131 * A122979 A122980 A012985

Adjacent sequences: A293756 A293757 A293758 * A293760 A293761 A293762

Keyword

nonn,more,hard

Author

Robert Price, Oct 15 2017

Extensions

Comments, Link and Example corrected by Robert Price, Jun 11 2018

Status

approved