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

Author

Patrick De Geest, Nov 16 2002

Keywords

• more
• nonn
• base

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

Examples

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

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

• 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.

Crossrefs

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

Programs

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 *)

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

Formula

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

Extensions

a(14) from Robert Price, Nov 23 2015

Name corrected by Jon E. Schoenfield, Oct 31 2018