A293856 Numbers k such that (32*10^k + 319)/9 is prime.

1, 4, 5, 7, 8, 10, 14, 20, 44, 76, 88, 110, 121, 1469, 1535, 5030, 16391, 19592, 25265, 25819, 54458, 68320

Offset

1,2

Comments

For k>1, numbers such that the digit 3 followed by k-2 occurrences of the digit 5 followed by the digits 91 is prime (see Example section).

a(23) > 2*10^5.

Links

Table of n, a(n) for n=1..22.

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

Makoto Kamada, Search for 35w91

Example

4 is in this sequence because (32*10^4 + 319)/9 = 35591 is prime.
Initial terms and primes associated:
a(1) = 1, 71;
a(2) = 4, 35591;
a(3) = 5, 355591;
a(4) = 7, 35555591;
a(5) = 8, 355555591; etc.

Mathematica

Select[Range[0, 100000], PrimeQ[(32*10^# + 319)/9] &]

Crossrefs

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

Sequence in context: A120163 A088763 A032722 * A098416 A005556 A159698

Adjacent sequences: A293853 A293854 A293855 * A293857 A293858 A293859

Keyword

nonn,more,hard

Author

Robert Price, Oct 17 2017

Status

approved