A082697 -id:A082697 - cp's OEIS frontend

A082714 Numbers n such that 2(10^n-1)/3+(10^(n-1)+1) or (6910^(n-1)+3)/9 is a plateau or depression prime.

5, 7, 55, 97, 455, 575, 3385, 11441, 12625, 19447, 35461, 81215, 95327

Offset: 1

Patrick De Geest, Apr 13 2003

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

			7 is a term because 2*(10^7-1)/3+(10^6+1) = 7666667.

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

Patrick De Geest, PDP Reference Table - 767.
Makoto Kamada, Prime numbers of the form 766...667.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056260.

35461 from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
Added two more terms from PDP table, by Patrick De Geest, Nov 04 2014
Edited by Ray Chandler, Nov 05 2014
Name clarified by Michel Marcus, Mar 27 2020

A082715 Numbers k such that (71*10^(k-1) - 17)/9 is a plateau prime.

Original entry on oeis.org

3, 5, 87, 113, 171, 567, 1689, 8903, 115811

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=5 -> (71*10^(5-1) - 17)/9 = 78887.

C. Caldwell and H. Dubner, The near repdigit primes A(n-k-1)B(1)A(k), especially 9(n-k-1)8(1)9(k), Journal of Recreational Mathematics, Volume 28, No. 1, 1996-97, pp. 1-9.

Patrick De Geest, PDP Reference Table - 787.
Makoto Kamada, Prime numbers of the form 788...887.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056262.

a(n) = A056262(n) + 2.

115811 from Ray Chandler, Aug 05 2011
a(2)=5 corrected by Patrick De Geest, Apr 28 2013
Edited by Ray Chandler, Nov 05 2014

A082716 Numbers k such that (72*10^(k-1) - 27)/9 is a plateau prime.

Original entry on oeis.org

3, 5, 29, 157, 323, 353, 1213, 1285, 7985, 15193, 84773, 119931, 148861

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=5 -> (72*10^(5-1) - 27)/9 = 79997.

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

Patrick De Geest, PDP Reference Table - 797.
Makoto Kamada, Prime numbers of the form 799...997.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056263.

a(n) = A056263(n) + 2.

a(11)=84773 from Ray Chandler, Jan 03 2011
a(12)=119931 from Ray Chandler, Apr 01 2011
a(13)=148861 from Ray Chandler, Apr 09 2011
Edited by Ray Chandler, Nov 04 2014

A082717 Numbers k such that (82*10^(k-1) + 71)/9 is a depression prime.

Original entry on oeis.org

3, 247, 1141, 10395, 43881

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=3 -> (82*10^(3-1) + 71)/9 = 919.

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

Patrick De Geest, PDP Reference Table - 919.
Makoto Kamada, Prime numbers of the form 911...119.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056264.

One more term from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Edited by Ray Chandler, Nov 04 2014

A082710 Numbers k such that (64*10^(k-1) + 53)/9 is a depression prime.

Original entry on oeis.org

10907, 499211

Offset: 1

Patrick De Geest, Apr 13 2003

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

Searched up to k=1200000 by Serge Batalov, Mar 02 2015

			a(1)=10907 -> (64*10^(10907-1) + 53)/9 = 7111...1117 or 10905 1's surrounded by two 7's.

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

Patrick De Geest, PDP Reference Table - 717.
Makoto Kamada, Prime numbers of the form 711...117.
Tanya Khovanova, Non Recursions
C. Rivera and J.C. Rosa, Puzzle 197. Always composite numbers?

Cf. A082697-A082720.

Edited by Ray Chandler, Nov 05 2014

Additional PRP term 499211 by Serge Batalov, Mar 01 2015

cp's OEIS Frontend

A082714 Numbers n such that 2*(10^n-1)/3+(10^(n-1)+1) or (69*10^(n-1)+3)/9 is a plateau or depression prime.

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A082715 Numbers k such that (71*10^(k-1) - 17)/9 is a plateau prime.

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A082716 Numbers k such that (72*10^(k-1) - 27)/9 is a plateau prime.

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A082717 Numbers k such that (82*10^(k-1) + 71)/9 is a depression prime.

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A082710 Numbers k such that (64*10^(k-1) + 53)/9 is a depression prime.

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A082714 Numbers n such that 2(10^n-1)/3+(10^(n-1)+1) or (6910^(n-1)+3)/9 is a plateau or depression prime.