A077784 Numbers k such that (10^k - 1)/3 + 2*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 5, 35, 159, 237, 325, 355, 371, 481, 1649, 3641, 4709, 269623

Offset

1,1

Comments

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

a(13) > 2*10^5. - Robert Price, Apr 03 2016

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..13.

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

Makoto Kamada, Prime numbers of the form 33...33533...33

Index entries for primes involving repunits.

Formula

a(n) = 2*A183175(n) + 1.

Example

5 is a term because (10^5 - 1)/3 + 2*10^2 = 33533.

Mathematica

Do[ If[ PrimeQ[(10^n + 6*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 4800, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Crossrefs

Partial sums of S(n, x), for x=1...9: A021823, A000217, A027941, A061278, A089817, A053142, A092521, A076765, A092420.

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

Sequence in context: A173092 A057908 A120828 * A325582 A145640 A222496

Adjacent sequences: A077781 A077782 A077783 * A077785 A077786 A077787

Keyword

more,nonn,base

Author

Patrick De Geest, Nov 16 2002

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018

a(13) from Robert Price, Aug 03 2024

Status

approved