A089675 Numbers k such that 10^k - 3 is prime.

1, 2, 3, 17, 140, 990, 1887, 3530, 5996, 13820, 21873, 26045, 87720, 232599, 480684, 538640

Offset: 1

Author

Michael Gottlieb (mzrg(AT)verizon.net), Jan 05 2004

Keywords

• more
• nonn

Comments

Numbers k such that 9*R_k - 2 is a prime number, where R_k = 11...1 is the repunit (A002275) of length k.

If k is in the sequence (10^k-3 is prime) and m=3*(10^k-3) then phi(m)=reversal(m), i.e., m is in the sequence A069215. - Farideh Firoozbakht, Dec 25 2004

No further terms for k <= 407197, see Kamada link.

Examples

			10^2 - 3 = 97 is a prime number (in fact all terms are the largest less than 10^k).
		

Links

• Makoto Kamada, Prime numbers of the form 99...997.
• Index entries for primes involving repunits.

Crossrefs

Cf. A002275, A056662, A069215, A093172, A101700.

Programs

Mathematica

m = 1000; For[n = 1, n < m, If[PrimeQ[10^n - 3], Print[n]]; n++]

Formula

a(n) = A056662(n) + 1.

Extensions

a(8) from Robert G. Wilson v, Jan 14 2004

a(9) and a(10) from Gabriel Cunningham (gcasey(AT)mit.edu), Mar 06 2004

a(11) from Gabriel Cunningham (gcasey(AT)mit.edu), Mar 13 2004

a(12) from Henri Lifchitz.

Edited by Patrick De Geest, Dec 28 2004

Edited by Ray Chandler, Dec 23 2010

a(15) from Paul Bourdelais, Jan 06 2021

a(16) from Paul Bourdelais, Jan 28 2021