A089675 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..16.

Makoto Kamada, Prime numbers of the form 99...997.

Index entries for primes involving repunits.

FORMULA

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

EXAMPLE

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

MATHEMATICA

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

CROSSREFS

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

Sequence in context: A259535 A328340 A042978 * A041383 A042903 A367686

Adjacent sequences: A089672 A089673 A089674 * A089676 A089677 A089678

KEYWORD

more,nonn

AUTHOR

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

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

STATUS

approved