A183182 -id:A183182 - 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.

A077793 Numbers k such that 7*(10^k - 1)/9 + 10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

3, 7, 79, 109, 337, 481, 10657, 12319, 49351, 104455, 227775

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 7*(10^7 - 1)/9 + 10^3 = 7778777.

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^n + 9*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 12400, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A183182(n) + 1.

Name corrected by Jon E. Schoenfield, Oct 31 2018
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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