A077787 Numbers k such that (10^k - 1)/9 + 5*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

21, 29, 81, 119, 321, 825, 1121, 2579, 3693

Offset

1,1

Comments

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

a(10) > 4*10^5. - _Robert Price, Jan 23 2025

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..9.

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)

Makoto Kamada, Prime numbers of the form 11...11611...11

Index entries for primes involving repunits.

Formula

a(n) = 2*A107126(n) + 1.

Example

21 is a term because (10^21 - 1)/9 + 5*10^10 = 111111111161111111111.

Mathematica

Do[ If[ PrimeQ[(10^n + 45*10^Floor[n/2] - 1)/9], Print[n]], {n, 3, 4000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Crossrefs

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

Sequence in context: A004196 A211253 A209975 * A039372 A043195 A043975

Adjacent sequences: A077784 A077785 A077786 * A077788 A077789 A077790

Keyword

more,nonn,base

Author

Patrick De Geest, Nov 16 2002

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

Status

approved