A093172 -id:A093172 - cp's OEIS frontend

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

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

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.

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

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

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

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

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

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

A240696 Prime numbers n such that replacing each digit d in the decimal expansion of n with its 9's complement produces a prime.

Original entry on oeis.org

2, 7, 97, 997, 99999999999999997

Offset: 1

Michel Lagneau, Apr 10 2014

a(n) = {2} union {primes of the form 10^n - 3} = {2} union {A093172}.
Primes p such that A061601(p) is also prime.
The next term has 140 digits.

			997 is in the sequence because 997 becomes (002) = 2, which is prime.

Cf. A093172, A173833.

lst={};f[n_]:=Block[{a=IntegerDigits[Prime[n]],b="",k=1,l},l=Length[a];While[k

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula

Extensions