A183178 -id:A183178 - cp's OEIS frontend

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).

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

A332172 a(n) = 7(10^(2n+1)-1)/9 - 510^n.

Original entry on oeis.org

2, 727, 77277, 7772777, 777727777, 77777277777, 7777772777777, 777777727777777, 77777777277777777, 7777777772777777777, 777777777727777777777, 77777777777277777777777, 7777777777772777777777777, 777777777777727777777777777, 77777777777777277777777777777, 7777777777777772777777777777777

Offset: 0

M. F. Hasler, Feb 06 2020

Indices of prime terms: {0, 1, 3, 7, 10, 12, 480, 949, ...} = A183178.

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

Cf. A138148 (cyclops numbers with binary digits only).
Cf. A332171 (analog with middle digit 1).
Cf. (A077777-1)/2 = A183178: indices of primes.
Cf. A002275 (repunits R_n = [10^n/9]), A002281 (7*R_n), A011557 (10^n).
Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

A332172 := n -> 7*(10^(n*2+1)-1)/9 -5*10^n;

Array[7 (10^(2 # +1)-1)/9 -5*10^# &, 15, 0]

apply( {A332172(n)=10^(n*2+1)\9*7-5*10^n}, [0..25])

def A332172(n): return 10**(n*2+1)//9*7-5*10^n

a(n) = 7*A138148(n) + 2*10^n.
G.f.: (2 + 505*x - 1200*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.

cp's OEIS Frontend

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).

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A332172 a(n) = 7(10^(2n+1)-1)/9 - 510^n.

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cp's OEIS Frontend

A077777 Numbers k such that 7*(10^k - 1)/9 - 5*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

PARI

Formula

Extensions

A332172 a(n) = 7*(10^(2n+1)-1)/9 - 5*10^n.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Python

Formula

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).

A332172 a(n) = 7(10^(2n+1)-1)/9 - 510^n.