A077781 Numbers k such that 7*(10^k - 1)/9 - 3*10^floor(k/2) is a palindromic wing prime (also known as near-repdigit palindromic prime).

5, 7, 13, 47, 73, 139, 1123, 1447, 6877, 8209, 18041, 27955, 39311, 64801

Offset

1,1

Comments

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

a(15) > 2*10^5. - Robert Price, Nov 23 2015

References

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.

Links

Table of n, a(n) for n=1..14.

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.

Formula

a(n) = 2*A183179(n) + 1.

Example

7 is a term because 7*(10^7 - 1)/9 - 3*10^3 = 7774777.

Mathematica

Do[ If[ PrimeQ[(7*10^n - 27*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 39400, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Prog

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

Crossrefs

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

Sequence in context: A064600 A174874 A109904 * A102872 A102873 A356847

Adjacent sequences: A077778 A077779 A077780 * A077782 A077783 A077784

Keyword

more,nonn,base

Author

Patrick De Geest, Nov 16 2002

Extensions

a(14) from Robert Price, Nov 23 2015

Name corrected by Jon E. Schoenfield, Oct 31 2018

Status

approved