A077793 -id:A077793 - cp's OEIS frontend

A332178 a(n) = 7*(10^(2n+1)-1)/9 + 10^n.

8, 787, 77877, 7778777, 777787777, 77777877777, 7777778777777, 777777787777777, 77777777877777777, 7777777778777777777, 777777777787777777777, 77777777777877777777777, 7777777777778777777777777, 777777777777787777777777777, 77777777777777877777777777777, 7777777777777778777777777777777

Offset: 0

M. F. Hasler, Feb 08 2020

See A183182 = {1, 3, 39, 54, 168, 240, ...} for the indices of primes.

Makoto Kamada, Factorization of 77...77877...77, updated Dec 11 2018.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077793-1)/2 = A183182: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

A332178 := n -> 7*(10^(n*2+1)-1)/9 + 10^n;

Array[7 (10^(2 # + 1) - 1)/9 + 10^# &, 15, 0]

apply( {A332178(n)=10^(n*2+1)\9*7+10^n}, [0..15])

def A332178(n): return 10**(n*2+1)//9*7+10^n

a(n) = 7*A138148(n) + 8*10^n.
G.f.: (8 - 101*x - 600*x^2)/((1 - x)*(1 - 10*x)*(1 - 100*x)).
a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

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

A332178 a(n) = 7*(10^(2n+1)-1)/9 + 10^n.

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

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cp's OEIS Frontend

A332178 a(n) = 7*(10^(2n+1)-1)/9 + 10^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

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

Views

Author

Keywords

References

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

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