A077785 Odd numbers k such that the palindromic wing number (a.k.a. near-repdigit palindrome) 7*(10^k - 1)/9 - 2*10^((k-1)/2) is prime.

3, 15, 27, 117, 259, 507, 3315, 4489, 4875, 15849, 19807, 23799, 36315, 37915, 47331, 211219

Offset

1,1

Comments

Original name was "Palindromic wing primes (a.k.a. near-repdigit palindromes) of the form 7*(10^a(n)-1)/9-2*10^[ a(n)/2 ]."

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

a(16) > 2*10^5. - Robert Price, Jun 23 2017

1 could be considered part of this sequence since the formula evaluates to 5 which is a degenerate form of the near-repdigit palindrome 777...77577...777 that has zero occurrences of the digit 7. - Robert Price, Jun 23 2017

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..16.

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

Makoto Kamada, Prime numbers of the form 77...77577...77

Index entries for primes involving repunits.

Formula

a(n) = 2*A183180(n) + 1.

Example

15 is in the sequence because 7*(10^15 - 1)/9 - 2*10^7 = 777777757777777 is prime.

Mathematica

Do[ If[ PrimeQ[(7*10^n - 18*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 40000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

Crossrefs

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

Sequence in context: A347536 A002259 A050848 * A222291 A015646 A242571

Adjacent sequences: A077782 A077783 A077784 * A077786 A077787 A077788

Keyword

more,nonn,base

Author

Patrick De Geest, Nov 16 2002

Extensions

a(15) from Robert Price, Jun 23 2017

Example edited by Jon E. Schoenfield, Jun 23 2017

Name edited by Jon E. Schoenfield, Jun 24 2017

a(16) from Robert Price, Oct 12 2023

Status

approved