A183183 -id:A183183 - cp's OEIS frontend

A332179 a(n) = 7(10^(2n+1)-1)/9 + 210^n.

9, 797, 77977, 7779777, 777797777, 77777977777, 7777779777777, 777777797777777, 77777777977777777, 7777777779777777777, 777777777797777777777, 77777777777977777777777, 7777777777779777777777777, 777777777777797777777777777, 77777777777777977777777777777, 7777777777777779777777777777777

Offset: 0

M. F. Hasler, Feb 08 2020

See A183183 = {1, 2, 8, 19, 20, 212, 280, ...} for the indices of primes.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. A138148 (cyclops numbers with binary digits only).
Cf. (A077796-1)/2 = A183183: indices of primes.
Cf. A002275 (repunits R_n = [10^n/9]), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332178 (variants with different middle digit 1, ..., 8).

A332179 := n -> 7*(10^(n*2+1)-1)/9 + 2*10^n;

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

apply( {A332179(n)=10^(n*2+1)\9*7+2*10^n}, [0..15])

def A332179(n): return 10**(n*2+1)//9*7+2*10^n

a(n) = 7*A138148(n) + 9*10^n.
G.f.: (9 - 202*x - 500*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.

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

cp's OEIS Frontend

A332179 a(n) = 7(10^(2n+1)-1)/9 + 210^n.

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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).

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cp's OEIS Frontend

A332179 a(n) = 7*(10^(2n+1)-1)/9 + 2*10^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

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).

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A332179 a(n) = 7(10^(2n+1)-1)/9 + 210^n.

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).