A107127 -id:A107127 - cp's OEIS frontend

A077795 Numbers k such that (10^k - 1)/9 + 8*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 9, 53, 375, 453, 1749, 26619, 68033, 85179

Offset: 1

Patrick De Geest, Nov 16 2002

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

a(10) > 400000. - Robert Price, Jan 30 2025

			9 is a term because (10^9 - 1)/9 + 8*10^4 = 111191111.

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...11911...11
Index entries for primes involving repunits.

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

a(n) = 2*A107649(n) + 1.

Name corrected by Jon E. Schoenfield, Oct 30 2018

a(8)-a(9) from Robert Price, Jan 30 2025

A077796 Numbers k such that 7(10^k - 1)/9 + 210^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 5, 17, 39, 41, 425, 561, 1775, 2043, 11031, 16233, 23705

Offset: 1

Patrick De Geest, Nov 16 2002

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

a(13) > 2*10^5. - Robert Price, Jan 19 2016

			17 is a term because 7*(10^17 - 1)/9 + 2*10^8 = 77777777977777777.

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^n + 18*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 23800, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A183183(n) + 1.

Name corrected by Jon E. Schoenfield, Oct 31 2018

A183175 Numbers k such that (10^(2k+1) + 6*10^k - 1)/3 is prime.

Original entry on oeis.org

1, 2, 17, 79, 118, 162, 177, 185, 240, 824, 1820, 2354, 134811

Offset: 1

Ray Chandler, Dec 28 2010

a(13) > 10^5. - Robert Price, Apr 03 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 33...33533...33.
Index entries for primes involving repunits.

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

Do[If[PrimeQ[(10^(2n + 1) + 6*10^n - 1)/3], Print[n]], {n, 3000}]

is(n)=ispseudoprime((10^(2*n+1)+6*10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077784(n) - 1)/2.

a(13) from Robert Price, Aug 03 2024

A183176 Numbers k such that (10^(2k+1) + 12*10^k - 1)/3 is prime.

Original entry on oeis.org

1, 3, 7, 11, 13, 17, 29, 31, 33, 77, 933, 1555, 11758, 117707

Offset: 1

Ray Chandler, Dec 28 2010

a(14) > 100000. - Robert Price, Dec 29 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 33...33733...33.
Index entries for primes involving repunits.

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

Do[If[PrimeQ[(10^(2n + 1) + 12*10^n - 1)/3], Print[n]], {n, 3000}]

is(n)=ispseudoprime((10^(2*n+1)+12*10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077790(n) - 1)/2.

a(14) from Robert Price, Oct 30 2023

A183177 Numbers n such that (10^(2n+1)+15*10^n-1)/3 is prime.

Original entry on oeis.org

1, 7, 85, 94, 273, 356, 1077, 1797, 6758, 30232

Offset: 1

Ray Chandler, Dec 28 2010

a(11) > 10^5. - Robert Price, Apr 21 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 33...33833...33
Index entries for primes involving repunits.

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

Do[If[PrimeQ[(10^(2n + 1) + 15*10^n - 1)/3], Print[n]], {n, 3000}]

is(n)=ispseudoprime((10^(2*n+1)+15*10^n-1)/3) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077792(n)-1)/2.

a(10) from Robert Price, Apr 21 2016

A183178 Numbers k such that 7(10^(2k+1)-1)/9 - 5*10^k is prime.

Original entry on oeis.org

0, 1, 3, 7, 10, 12, 480, 949, 1945, 7548, 8923

Offset: 1

Ray Chandler, Dec 28 2010

Original name: Numbers n such that (7*10^(2n+1)-45*10^n-7)/9 is prime.

a(12) > 10^5. - Robert Price, Nov 02 2015

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^(2n + 1) - 45*10^n - 7)/9], Print[n]], {n, 3000}]

is(n)=ispseudoprime((7*10^(2*n+1)-45*10^n-7)/9) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077777(n-1)-1)/2 for n>1.

Name edited and a(1) = 0 inserted by M. F. Hasler, Feb 07 2020

A183179 Numbers n such that 7(10^(2n+1)-1)/9 - 310^n is prime.

Original entry on oeis.org

2, 3, 6, 23, 36, 69, 561, 723, 3438, 4104, 9020, 13977, 19655, 32400

Offset: 1

Ray Chandler, Dec 28 2010

Original name: Numbers n such that (7*10^(2n+1)-27*10^n-7)/9 is prime.

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

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^(2n + 1) - 27*10^n - 7)/9], Print[n]], {n, 3000}]

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

a(n) = (A077781(n)-1)/2.

a(14) from Robert Price, Nov 23 2015

A183180 Numbers k such that (710^(2k+1) - 1810^k - 7)/9 is prime.

Original entry on oeis.org

0, 1, 7, 13, 58, 129, 253, 1657, 2244, 2437, 7924, 9903, 11899, 18157, 18957, 23665, 105609

Offset: 1

Ray Chandler, Dec 28 2010

a(17) > 10^5. - Robert Price, Jun 23 2017

0 could be considered part of this sequence since the formula evaluates to 5 which is a degenerate form of the near-repdigit palindrome 777...77577...777 with 0 occurrences of the digit 7. - Robert Price, Jun 23 2017

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...77577...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) = (A077785(n) - 1)/2.

a(16) from Robert Price, Jun 23 2017

a(17) from Robert Price, Oct 12 2023

A183181 Numbers k such that (710^(2k+1) - 9*10^k - 7)/9 is prime.

Original entry on oeis.org

4, 5, 8, 11, 1244, 1685, 2009, 14657, 15118, 20332, 50830, 75062

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 77...77677...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) - 9*10^n - 7)/9], Print[n]], {n, 3000}]

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

a(n) = (A077788(n) - 1)/2.

a(10) from Robert Price, Oct 07 2023
a(11) from Robert Price, Oct 17 2023
a(12) from Robert Price, Dec 06 2023

A183182 Numbers k such that (710^(2k+1) + 9*10^k - 7)/9 is prime.

Original entry on oeis.org

1, 3, 39, 54, 168, 240, 5328, 6159, 24675, 52227, 113887

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 77...77877...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) + 9*10^n - 7)/9], Print[n]], {n, 3000}]

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

a(n) = (A077793(n) - 1)/2.

a(9) from Robert Price, Oct 07 2023
a(10) from Robert Price, Oct 30 2023
a(11) from Robert Price, Aug 03 2024

cp's OEIS Frontend

A077795 Numbers k such that (10^k - 1)/9 + 8*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

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A077796 Numbers k such that 7*(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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A183175 Numbers k such that (10^(2k+1) + 6*10^k - 1)/3 is prime.

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A183176 Numbers k such that (10^(2k+1) + 12*10^k - 1)/3 is prime.

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A183177 Numbers n such that (10^(2n+1)+15*10^n-1)/3 is prime.

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PARI

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A183178 Numbers k such that 7*(10^(2*k+1)-1)/9 - 5*10^k is prime.

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Programs

Mathematica

PARI

Formula

Extensions

A183179 Numbers n such that 7*(10^(2n+1)-1)/9 - 3*10^n is prime.

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A077796 Numbers k such that 7(10^k - 1)/9 + 210^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

A183178 Numbers k such that 7(10^(2k+1)-1)/9 - 5*10^k is prime.

A183179 Numbers n such that 7(10^(2n+1)-1)/9 - 310^n is prime.

A183180 Numbers k such that (710^(2k+1) - 1810^k - 7)/9 is prime.

A183181 Numbers k such that (710^(2k+1) - 9*10^k - 7)/9 is prime.

A183182 Numbers k such that (710^(2k+1) + 9*10^k - 7)/9 is prime.