A183187 -id:A183187 - cp's OEIS frontend

A183184 Numbers n such that 10^(2n+1)-8*10^n-1 is prime.

1, 5, 13, 43, 169, 181, 1579, 18077, 22652, 157363

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...99199...99
Index entries for primes involving repunits.

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

Do[If[PrimeQ[10^(2n + 1) - 8*10^n - 1], Print[n]], {n, 3000}]

is(n)=ispseudoprime(10^(2*n+1)-8*10^n-1) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077776(n)-1)/2.

Added one more term from PWP table, by Patrick De Geest, Nov 05 2014

A077779 Numbers k such that (10^k - 1)/9 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 5, 39, 195, 19637

Offset: 1

Patrick De Geest, Nov 16 2002

Prime versus probable prime status and proofs are given in the author's table.
a(6) > 2*10^5. - Robert Price, Apr 02 2016
The number k = 1 would also correspond to a prime, 3, but not "near-repdigit" or "wing" in a strict sense. - M. F. Hasler, Feb 09 2020

			5 is a term because (10^5 - 1)/9 + 2*10^2 = 11311.

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...11311...11
Index entries for primes involving repunits.

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

See A332113 for the (prime and composite) near-repunit palindromes 1..131..1.

Do[ If[ PrimeQ[(10^n + 18*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 20000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A107123(n+1) + 1.

Name corrected by Jon E. Schoenfield, Oct 31 2018

A077780 Numbers k such that (10^k - 1)/9 + 3*10^floor(k/2) is palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

5, 7, 65, 91, 3089

Offset: 1

Patrick De Geest, Nov 16 2002

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

			7 is a term because (10^7 - 1)/9 + 3*10^3 = 1114111.

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...11411...11
Index entries for primes involving repunits.

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

Do[ If[ PrimeQ[(10^n + 27*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 3100, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A107124(n) + 1.

Name corrected by Jon E. Schoenfield, Oct 31 2018

A077783 Numbers k such that (10^k-1)/9 + 4*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 15, 91, 231, 1363, 2497, 4963, 5379, 12397, 26395, 120253, 200145

Offset: 1

Patrick De Geest, Nov 16 2002

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

a(13) > 200466. - _Robert Price, Sep 05 2023

			15 is a term because (10^15 - 1)/9 + 4*10^7 = 111111151111111.

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...11511...11
Index entries for primes involving repunits.

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

[n: n in [3..2000 by 2] | IsPrime((10^n+36*10^(n div 2)-1) div 9)]; // Vincenzo Librandi, Oct 13 2015

Do[ If[ PrimeQ[(10^n + 36*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 26400, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A107125(n) + 1.

a(11) from Robert Price, Oct 12 2015
Name edited by Jon E. Schoenfield, Oct 13 2015
a(12) from Robert Price, Sep 05 2023

A107125 Numbers k such that (10^(2k+1) + 3610^k - 1)/9 is prime.

Original entry on oeis.org

0, 1, 7, 45, 115, 681, 1248, 2481, 2689, 6198, 13197, 60126, 100072

Offset: 1

Farideh Firoozbakht, May 19 2005

k is in the sequence iff the palindromic number 1(k).5.1(k) is prime (dot between numbers means concatenation). If k is in the sequence then k is not of the forms 3m+2, 18m+12, 18m+14, 22m+4, 22m+6, etc. (the proof is easy).

a(14) > 100233. - _Robert Price, Sep 05 2023

			1248 is in the sequence because (10^(2*1248+1)+36*10^1248-1)/9=1(1248).5.1(1248) is prime.

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...11511...11
Index entries for primes involving repunits.

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

[n: n in [0..700] | IsPrime((10^(2*n+1)+36*10^n-1) div 9)]; // Vincenzo Librandi, Oct 13 2015

Do[If[PrimeQ[(10^(2n + 1) + 36*10^n - 1)/9], Print[n]], {n, 2200}]

is(n)=ispseudoprime((10^(2*n+1)+36*10^n-1)/9) \\ Charles R Greathouse IV, Jun 06 2017

a(n) = (A077783(n)-1)/2.

Edited by Ray Chandler, Dec 28 2010
a(12) from Robert Price, Oct 12 2015
a(13) from Robert Price, Sep 05 2023

A107126 Numbers n such that (10^(2n+1)+45*10^n-1)/9 is prime.

Original entry on oeis.org

10, 14, 40, 59, 160, 412, 560, 1289, 1846

Offset: 1

Farideh Firoozbakht, May 19 2005

n is in the sequence iff the palindromic number 1(n).6.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m + 1, 16m + 2, 16m + 5, 22m + 1, 22m + 9, etc. (the proof is easy).

a(10) > 200000 - Robert Price, Jan 23 2025

			14 is in the sequence because (10^(2*14+1)+45*10^14-1)/9=1(14).6.1(14) = 11111111111111611111111111111 is prime.

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^(2n + 1) + 45*10^n - 1)/9], Print[n]], {n, 2500}]
Position[Table[FromDigits[Join[PadRight[{},n,1],{6},PadRight[{},n,1]]],{n,1850}],?PrimeQ]//Flatten (* _Harvey P. Dale, Jun 22 2017 *)

is(n)=ispseudoprime((10^(2*n+1)+45*10^n-1)/9) \\ Charles R Greathouse IV, Jun 06 2017

a(n) = (A077787(n)-1)/2.

Edited by Ray Chandler, Dec 28 2010.

A077777 Numbers k such that 7(10^k - 1)/9 - 510^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 7, 15, 21, 25, 961, 1899, 3891, 15097, 17847

Offset: 1

Patrick De Geest, Nov 16 2002

Prime versus probable prime status and proofs are given in the author's table.
a(11) > 2*10^5. - Robert Price, Nov 02 2015
A183178(1) = 0 would correspond to an initial term 1 in this sequence which yields the prime 2 (which has a "wing" of length 0 and is a palindrome and repdigit but not near-repdigit). - M. F. Hasler, Feb 08 2020

			15 is a term because 7*(10^15 - 1)/9 - 5*10^7 = 777777727777777.

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...77277...77
Index entries for primes involving repunits.

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

Do[ If[ PrimeQ[(7*10^n - 45*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 1000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

for(k=1,oo,ispseudoprime(10^k\9*7-5*10^(k\2))&&print1(k",")) \\ M. F. Hasler, Feb 08 2020

a(n) = 2*A183178(n+1) + 1.

Name corrected by Jon E. Schoenfield, Oct 31 2018

A077778 Numbers k such that (10^k - 1) - 7*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 17, 19, 705, 1061, 1395, 2631, 3837, 5749, 11753, 13537, 125877, 269479

Offset: 1

Patrick De Geest, Nov 16 2002

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

			17 is a term because (10^17 - 1) - 7*10^8 = 99999999299999999.

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...99299...99
Index entries for primes involving repunits.

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

Do[ If[ PrimeQ[10^n - 7*10^Floor[n/2] - 1], Print[n]], {n, 3, 14600, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A115073(n) + 1.

Two more terms from PWP table added by Patrick De Geest, Nov 05 2014

Name corrected by Jon E. Schoenfield, Oct 31 2018

A077781 Numbers k such that 7(10^k - 1)/9 - 310^floor(k/2) is a palindromic wing prime (also known as near-repdigit palindromic prime).

Original entry on oeis.org

5, 7, 13, 47, 73, 139, 1123, 1447, 6877, 8209, 18041, 27955, 39311, 64801

Offset: 1

Patrick De Geest, Nov 16 2002

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

a(15) > 2*10^5. - Robert Price, Nov 23 2015

			7 is a term because 7*(10^7 - 1)/9 - 3*10^3 = 7774777.

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, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 77...77477...77
Index entries for primes involving repunits.

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

Do[ If[ PrimeQ[(7*10^n - 27*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 39400, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

for(n=1, 1e3, if(ispseudoprime((7*10^(2*n+1)-27*10^n-7)/9), print1(2*n+1, ", "))) \\ Altug Alkan, Nov 23 2015

a(n) = 2*A183179(n) + 1.

a(14) from Robert Price, Nov 23 2015

Name corrected by Jon E. Schoenfield, Oct 31 2018

A077782 Numbers k such that (10^k - 1) - 5*10^floor(m/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

29, 45, 73, 209, 2273, 35729, 50897

Offset: 1

Patrick De Geest, Nov 16 2002

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

			29 is a term because (10^29 - 1) - 5*10^14 = 99999999999999499999999999999.

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^n - 5*10^Floor[n/2] - 1], Print[n]], {n, 3, 50900, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A183185(n) + 1.

Name corrected by Jon E. Schoenfield, Oct 31 2018

cp's OEIS Frontend

A183184 Numbers n such that 10^(2n+1)-8*10^n-1 is prime.

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A077779 Numbers k such that (10^k - 1)/9 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

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A077780 Numbers k such that (10^k - 1)/9 + 3*10^floor(k/2) is palindromic wing prime (a.k.a. near-repdigit palindromic prime).

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A077783 Numbers k such that (10^k-1)/9 + 4*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

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A107125 Numbers k such that (10^(2*k+1) + 36*10^k - 1)/9 is prime.

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Programs

Magma

Mathematica

PARI

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A107126 Numbers n such that (10^(2n+1)+45*10^n-1)/9 is prime.

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PARI

A107125 Numbers k such that (10^(2k+1) + 3610^k - 1)/9 is prime.

A077777 Numbers k such that 7(10^k - 1)/9 - 510^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

A077781 Numbers k such that 7(10^k - 1)/9 - 310^floor(k/2) is a palindromic wing prime (also known as near-repdigit palindromic prime).