A082698 -id:A082698 - cp's OEIS frontend

A082697 Numbers k such that (4*10^(k-1) - 7)/3 is a plateau prime.

3, 5, 7, 95, 161, 361, 1471, 2899, 3095, 3113, 15699, 17957, 42263, 111033

Offset: 1

Patrick De Geest, Apr 13 2003

Prime versus probable prime status and proofs are given in the author's table.

			k=7 -> (4*10^(7-1) - 7)/3 = 1333331.

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Patrick De Geest, PDP Reference Table - 131.
Makoto Kamada, Prime numbers of the form 133...331.
Index entries for primes involving repunits.

Cf. A056244, A068645, A082698-A082720.

a(n) = A056244(n+1) + 2.

a(13)=42263 from Patrick De Geest, Oct 03 2004
a(14)=111033 from Ray Chandler, Apr 14 2011
Edited by Ray Chandler, Nov 04 2014

A056245 Indices of primes in sequence defined by A(0) = 11, A(n) = 10*A(n-1) + 31 for n > 0.

Original entry on oeis.org

0, 5, 65, 1253, 8405, 67037

Offset: 1

Robert G. Wilson v, Aug 18 2000

Numbers n such that (130*10^n - 31)/9 is prime.
Numbers n such that digit 1 followed by n >= 0 occurrences of digit 4 followed by digit 1 is prime.
Numbers corresponding to terms <= 1253 are certified primes. For larger numbers see P. De Geest, PDP Reference Table.
a(7) > 2*10^5. - Tyler Busby, Feb 01 2023

			1444441 is prime, hence 5 is a term.

Klaus Brockhaus and Walter Oberschelp, Zahlenfolgen mit homogenem Ziffernkern, MNU 59/8 (2006), pp. 462-467.

Patrick De Geest, PDP Reference Table - 141.
Makoto Kamada, Prime numbers of the form 144...441.
Index entries for primes involving repunits.

Cf. A000533, A002275, A082698.

[n: n in [0..500] | IsPrime((130*10^n-31) div 9)]; // Vincenzo Librandi, Nov 03 2014

Select[Range[0, 2000], PrimeQ[(130 10^# - 31) / 9] &] (* Vincenzo Librandi, Nov 03 2014 *)

a=11;for(n=0,1500,if(isprime(a),print1(n,","));a=10*a+31)

for(n=0,1500,if(isprime((130*10^n-31)/9),print1(n,",")))

a(n) = A082698(n-1) - 2 for n > 1.

Additional comments from Klaus Brockhaus and Walter Oberschelp (oberschelp(AT)informatik.rwth-aachen.de), Dec 28 2004
Edited by N. J. A. Sloane, Jun 15 2007
8405 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Added one more term from the PDP table and updated a link, by Patrick De Geest, Nov 02 2014
Edited by Ray Chandler, Nov 04 2014

cp's OEIS Frontend

A082697 Numbers k such that (4*10^(k-1) - 7)/3 is a plateau prime.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Formula

Extensions