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

1,1

Comments

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

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

References

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Links

Table of n, a(n) for n=1..12.

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.

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A319950 A336743 A034954 * A347319 A047019 A099251

Adjacent sequences: A077780 A077781 A077782 * A077784 A077785 A077786

Keyword

more,nonn,base

Author

Patrick De Geest, Nov 16 2002

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

Status

approved