A077775 Odd 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) of the form 3...313...3.

3, 7, 15, 123, 181, 185, 539, 597, 643, 743, 1553, 3135, 4769, 5133, 6177, 11733, 16103, 18997, 25271, 49025, 65043, 87965

Offset

1,1

Comments

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

a(23) > 2*10^5. - Robert Price, Jan 29 2016

Primes of the form (10^k-1)/3 - 2*10^floor(k/2) are obtained for k in (2, 3, 6, 7, 8, 10, 15, 22, 34, 123, 126, 144, 181, 185, 198, 534, 539, 597, 606, ...). For example (10^2 - 1)/3 - 2*10^1 = 13 is also prime. However, for even k the result is not palindromic. See A077775-A077798, A107123-A107127 for PWP's with digits other than 3 and 1. - M. F. Hasler, Mar 03 2019

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..22.

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

Makoto Kamada, Prime numbers of the form 33...33133...33

Index entries for primes involving repunits.

Formula

a(n) = 2*A183174(n) + 1.

Example

a(3) = 15 corresponds to the prime (10^15 - 1)/3 - 2*10^7 = 333333313333333.

Mathematica

Do[ If[ PrimeQ[(10^n - 6*10^Floor[n/2] - 1)/3], Print[n]], {n, 3, 49100, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Prog

(PARI) is(n)=bittest(n, 0)&&ispseudoprime(10^n\3-2*10^(n\2)) \\ M. F. Hasler, Mar 03 2019

Crossrefs

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

Sequence in context: A154795 A193831 A246719 * A197594 A206851 A033089

Adjacent sequences: A077772 A077773 A077774 * A077776 A077777 A077778

Keyword

more,nonn,base

Author

Patrick De Geest, Nov 16 2002

Extensions

a(21)-a(22) from Robert Price, Jan 29 2016

a(21) corrected by Robert Price, Feb 03 2016

Name corrected by Jon E. Schoenfield, Oct 31 2018

Name edited by M. F. Hasler, Mar 03 2019

Status

approved