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

Author

Patrick De Geest, Nov 16 2002

Keywords

• more
• nonn
• base

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

Examples

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

References

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

Links

• 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.

Crossrefs

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

Programs

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 *)

Formula

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

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