A082720 -id:A082720 - cp's OEIS frontend

A082706 Numbers k such that (31*10^(k-1) - 13)/9 is a plateau prime.

7, 13, 493, 5569, 24757

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=13 -> (31*10^(13-1) - 13)/9 = 3444444444443.

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

Patrick De Geest, PDP Reference Table - 343.
Makoto Kamada, Prime numbers of the form 344...443.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056253.

a(n) = A056253(n) + 2.

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Edited by Ray Chandler, Nov 05 2014

A082707 Numbers k such that (32*10^(k-1) - 23)/9 is a plateau prime.

Original entry on oeis.org

3, 9, 141, 231, 427, 463, 727, 1975, 7231, 45861, 47305

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=9 -> (32*10^(9-1) - 23)/9 = 355555553.

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

Patrick De Geest, PDP Reference Table - 353.
Makoto Kamada, Prime numbers of the form 355...553.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056254.

a(n) = A056254(n) + 2.

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008

Edited by Ray Chandler, Nov 05 2014

A082708 Numbers k such that (34*10^(k-1) - 43)/9 is a plateau prime.

Original entry on oeis.org

3, 15, 55, 69, 85, 87, 157, 2767, 3381, 3877, 5209, 10747, 15769, 31317, 40959, 45805, 46567, 51009, 80163

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=15 -> (34*10^(15-1) - 43)/9 = 377777777777773.

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

Patrick De Geest, PDP Reference Table - 373.
Makoto Kamada, Prime numbers of the form 377...773.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056255.

a(n) = A056255(n) + 2.

Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(18)=51009 from Ray Chandler, Nov 16 2010
a(19)=80163 from Ray Chandler, Dec 15 2010
Edited by Ray Chandler, Nov 05 2014

A082709 Numbers k such that (35*10^(k-1) - 53)/9 is a plateau prime.

Original entry on oeis.org

3, 13, 31, 61, 117, 291, 633, 1065, 1495, 5433, 7363

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=13 -> (35*10^(13-1) - 53)/9 = 3888888888883.

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

Patrick De Geest, PDP Reference Table - 383.
Makoto Kamada, Prime numbers of the form 388...883.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056256.

a(n) = A056256(n) + 2.

Edited by Ray Chandler, Nov 05 2014

A082711 Numbers k such that (65*10^(k-1) + 43)/9 is a depression prime.

Original entry on oeis.org

3, 5, 9, 29, 65, 725, 1787, 7277, 19463, 24215, 51779, 131393

Offset: 1

Patrick De Geest, Apr 13 2003

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

a(13) > 2*10^5. - Tyler Busby, Feb 01 2023

			k=9 -> (65*10^(9-1) + 43)/9 = 722222227.

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

Patrick De Geest, PDP Reference Table - 727.
Makoto Kamada, Prime numbers of the form 722...227.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056257.

a(n) = A056257(n) + 2.

Update from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(11)=51779 from Ray Chandler, Nov 16 2010
Edited by Ray Chandler, Nov 05 2014
a(12) from Tyler Busby, Feb 01 2023

A082712 Numbers k such that (67*10^(k-1) + 23)/9 is a depression prime.

Original entry on oeis.org

11, 31, 121, 485, 1487, 1579, 13673, 13811, 15095, 72773, 94212

Offset: 1

Patrick De Geest, Apr 13 2003

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

			k=11 -> (67*10^(11-1) + 23)/9 = 74444444447.

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

Patrick De Geest, PDP Reference Table - 747.
Makoto Kamada, Prime numbers of the form 744...447.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056258.

a(n) = A056258(n) + 2.

a(10)=72773 from Ray Chandler, Nov 16 2010
a(11)=94212 from Ray Chandler, Feb 21 2011
Edited by Ray Chandler, Nov 05 2014

A082713 Numbers k such that (68*10^(k-1) + 13)/9 is a depression prime.

Original entry on oeis.org

3, 5, 11, 21, 23, 59, 75, 83, 209, 351, 423, 3813, 3983, 20925, 23787, 38853, 56043, 68505, 74435

Offset: 1

Patrick De Geest, Apr 13 2003

Prime versus probable prime status and proofs are given in the De Geest link.

			k=21 -> (68*10^(21-1) + 13)/9 = 755555555555555555557.

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 - 757.
Makoto Kamada, Prime numbers of the form 755...557.
Index entries for primes involving repunits.

Cf. A082697-A082720, A056259.

a(n) = A056259(n) + 2.

Updates from De Geest site by Herman Jamke (hermanjamke(AT)fastmail.fm), Jan 02 2008
a(17)=56043 and a(18)=68505 from Ray Chandler, Nov 16 2010
a(19)=74434 from Ray Chandler, Nov 17 2010
a(19) corrected by Patrick De Geest, Nov 04 2014
Edited by Ray Chandler, Nov 05 2014
Definition rewritten by Michel Marcus, Oct 27 2019

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.

Original entry on oeis.org

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

cp's OEIS Frontend

A082706 Numbers k such that (31*10^(k-1) - 13)/9 is a plateau prime.

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A082707 Numbers k such that (32*10^(k-1) - 23)/9 is a plateau prime.

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A082708 Numbers k such that (34*10^(k-1) - 43)/9 is a plateau prime.

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A082709 Numbers k such that (35*10^(k-1) - 53)/9 is a plateau prime.

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A082711 Numbers k such that (65*10^(k-1) + 43)/9 is a depression prime.

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A082712 Numbers k such that (67*10^(k-1) + 23)/9 is a depression prime.

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A082713 Numbers k such that (68*10^(k-1) + 13)/9 is a depression prime.

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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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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.