A270929 Numbers k such that (16*10^k - 31)/3 is prime.

1, 2, 3, 4, 15, 20, 24, 32, 38, 40, 63, 93, 104, 194, 208, 514, 535, 600, 928, 1300, 1485, 1780, 2058, 3060, 3356, 3721, 6662, 11552, 15482, 23000, 27375, 34748, 57219, 61251, 85221, 99656, 103214, 103244, 276537

Offset: 1

Author

Robert Price, Mar 26 2016

Keywords

• nonn
• base
• more

Comments

For k > 1, numbers k such that the digit 5 followed by k-2 occurrences of the digit 3 followed by the digits 23 is prime (see Example section).

a(40) > 3*10^5. - Robert Price, Jul 13 2023

Examples

			3 is in this sequence because (16*10^3 - 31)/3 = 5323 is prime.
Initial terms and associated primes:
a(1) = 1, 43;
a(2) = 2, 523;
a(3) = 3, 5323;
a(4) = 4, 53323;
a(5) = 15, 5333333333333323;
a(6) = 20, 533333333333333333323, etc.
		

Links

• Makoto Kamada, Search for 53w23.

Crossrefs

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

Programs

Mathematica

Select[Range[0, 100000], PrimeQ[(16*10^# - 31)/3] &]

PARI

isok(n) = ispseudoprime((16*10^n - 31)/3); \\ Michel Marcus, Mar 26 2016

Extensions

a(37)-a(38) from Robert Price, Mar 03 2019

a(39) from Robert Price, Jul 13 2023