A183187 -id:A183187 - cp's OEIS frontend

A183183 Numbers n such that (710^(2n+1)+1810^n-7)/9 is prime.

Original entry on oeis.org

1, 2, 8, 19, 20, 212, 280, 887, 1021, 5515, 8116, 11852

Offset: 1

Ray Chandler, Dec 28 2010

a(13) > 10^5. - Robert Price, Jan 19 2016

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

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 77...77977...77
Index entries for primes involving repunits.

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Do[If[PrimeQ[(7*10^(2n + 1) + 18*10^n - 7)/9], Print[n]], {n, 3000}]

is(n)=ispseudoprime((7*10^(2*n+1)+18*10^n-7)/9) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077796(n)-1)/2.

A183185 Numbers n such that 10^(2n+1)-5*10^n-1 is prime.

Original entry on oeis.org

14, 22, 36, 104, 1136, 17864, 25448

Offset: 1

Ray Chandler, Dec 28 2010

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

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 99...99499...99
Index entries for primes involving repunits.

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Do[If[PrimeQ[10^(2n + 1) - 5*10^n - 1], Print[n]], {n, 3000}]

is(n)=ispseudoprime(10^(2*n+1)-5*10^n-1) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077782(n)-1)/2.

A183186 Numbers k such that 10^(2k+1) - 4*10^k - 1 is prime.

Original entry on oeis.org

88, 112, 198, 622, 4228, 10052, 55862

Offset: 1

Ray Chandler, Dec 28 2010

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

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's).
Makoto Kamada, Prime numbers of the form 99...99599...99.
Index entries for primes involving repunits.

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Do[If[PrimeQ[10^(2n + 1) - 4*10^n - 1], Print[n]], {n, 3000}]

is(n)=ispseudoprime(10^(2*n+1)-4*10^n-1) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077786(n) - 1)/2.

A077787 Numbers k such that (10^k - 1)/9 + 5*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

21, 29, 81, 119, 321, 825, 1121, 2579, 3693

Offset: 1

Patrick De Geest, Nov 16 2002

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

a(10) > 4*10^5. - _Robert Price, Jan 23 2025

			21 is a term because (10^21 - 1)/9 + 5*10^10 = 111111111161111111111.

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

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 11...11611...11
Index entries for primes involving repunits.

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Do[ If[ PrimeQ[(10^n + 45*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 4000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A107126(n) + 1.

Name corrected by Jon E. Schoenfield, Oct 31 2018

A265383 Numbers k such that 10^k * (10^k - 1) - 1 is prime.

Original entry on oeis.org

1, 6, 9, 154, 253, 1114, 1390, 2618, 5611, 12871, 15286, 108609, 132574, 164369, 188484

Offset: 1

Serge Batalov, Dec 07 2015

The primes arising from this construction (e.g., 999998999999) are among the primes counted in A266148. In particular, it follows that A266148(a(n)) > 0. - David A. Corneth, May 19 2016

a(16) > 188484. - Ben Meekins, Sep 08 2018

			6 is in the sequence because 10^12 - 10^6 - 1 = 999998999999 is prime.

Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
M. Kamada, Near-repdigit-related prime numbers

Cf. similar sequences listed in A265481.
A098845: Similar sequence in base 2.
A183187: Numbers k such that 10^(2k+1)-10^k-1 is prime, palindromic.
A266148: Number of n-digit primes in which n-1 of the digits are 9's.

[n: n in [0..200] | IsPrime(10^n*(10^n-1)-1)]; // Vincenzo Librandi, Dec 08 2015

Select[Range[15000], PrimeQ[10^# (10^# - 1) - 1] &] (* Vincenzo Librandi, Dec 08 2015 *)

for(n=1,9999,if(ispseudoprime(10^n*(10^n-1)-1),print1(n", ")))

a(11) from Kazuyoshi Asao, Feb 11 2002
a(12) from Serge Batalov, Dec 25 2015
a(13) from Ben Meekins, Feb 16 2016
a(14) from Ben Meekins, Dec 17 2016
a(15) from Ben Meekins, Sep 08 2018

A213881 k such that 10^(2k+1)-j10^k-1 is prime for some j = 1, 2, 4, 5, 7 or 8.

Original entry on oeis.org

1, 5, 8, 9, 13, 14, 22, 26, 36, 43, 88, 104, 112, 118, 169, 181, 198, 352, 378, 530, 622, 697, 1136, 1246, 1315, 1579, 1798, 1918, 2874, 2917, 4228, 5876, 6768, 10052, 17864, 18077, 22652, 23034, 25448, 47509, 52140, 55862, 62938, 67404, 134739, 145126

Offset: 1

Pierre CAMI, Jun 23 2012

The j values are either 7 and 8 for k=1. For larger k, there is one j only: 8, 7, 7, 8, 5, 5, 1, 5, 8, 4, 5, 4, 2, 8, 8, 4, 7, 1, 7, 4, 7, 5, 1, 7, 8, 1, 7, 7, 1, 4, 7, 7, 4, 5, 8, 8, 1, 5, 1, 1, 4, 7, 1, 7, 2.

The next k is probably near 160000 to 200000

			10^3-7*10^1-1=929 prime as 10^3-8*10^1-1=919 so a(1)=1.

Chris Caldwell, Palindrome
Chris Caldwell, Daren Bedwell

Cf. A115073, A183187

cp's OEIS Frontend

A183183 Numbers n such that (7*10^(2n+1)+18*10^n-7)/9 is prime.

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A183185 Numbers n such that 10^(2n+1)-5*10^n-1 is prime.

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A183186 Numbers k such that 10^(2k+1) - 4*10^k - 1 is prime.

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A077787 Numbers k such that (10^k - 1)/9 + 5*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

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A265383 Numbers k such that 10^k * (10^k - 1) - 1 is prime.

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A213881 k such that 10^(2*k+1)-j*10^k-1 is prime for some j = 1, 2, 4, 5, 7 or 8.

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A183183 Numbers n such that (710^(2n+1)+1810^n-7)/9 is prime.

A213881 k such that 10^(2k+1)-j10^k-1 is prime for some j = 1, 2, 4, 5, 7 or 8.