A077783 Numbers k such that (10^k-1)/9 + 4*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 15, 91, 231, 1363, 2497, 4963, 5379, 12397, 26395, 120253, 200145

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(13) > 200466. - _Robert Price, Sep 05 2023

Examples

			15 is a term because (10^15 - 1)/9 + 4*10^7 = 111111151111111.
		

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 11...11511...11
• Index entries for primes involving repunits.

Crossrefs

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

Programs

Magma

[n: n in [3..2000 by 2] | IsPrime((10^n+36*10^(n div 2)-1) div 9)]; // Vincenzo Librandi, Oct 13 2015

Mathematica

Do[ If[ PrimeQ[(10^n + 36*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 26400, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Formula

a(n) = 2*A107125(n) + 1.

Extensions

a(11) from Robert Price, Oct 12 2015

Name edited by Jon E. Schoenfield, Oct 13 2015

a(12) from Robert Price, Sep 05 2023