A077778 Numbers k such that (10^k - 1) - 7*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 17, 19, 705, 1061, 1395, 2631, 3837, 5749, 11753, 13537, 125877, 269479

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.

Examples

			17 is a term because (10^17 - 1) - 7*10^8 = 99999999299999999.
		

References

• C. Caldwell and H. Dubner, "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 99...99299...99
• Index entries for primes involving repunits.

Crossrefs

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

Programs

Mathematica

Do[ If[ PrimeQ[10^n - 7*10^Floor[n/2] - 1], Print[n]], {n, 3, 14600, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A115073(n) + 1.

Extensions

Two more terms from PWP table added by Patrick De Geest, Nov 05 2014

Name corrected by Jon E. Schoenfield, Oct 31 2018