A077777 Numbers k such that 7*(10^k - 1)/9 - 5*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

3, 7, 15, 21, 25, 961, 1899, 3891, 15097, 17847

Offset: 1

Author

Patrick De Geest, Nov 16 2002

Keywords

• more
• nonn
• base

Comments

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

a(11) > 2*10^5. - Robert Price, Nov 02 2015

A183178(1) = 0 would correspond to an initial term 1 in this sequence which yields the prime 2 (which has a "wing" of length 0 and is a palindrome and repdigit but not near-repdigit). - M. F. Hasler, Feb 08 2020

Examples

			15 is a term because 7*(10^15 - 1)/9 - 5*10^7 = 777777727777777.
		

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...77277...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 - 45*10^Floor[n/2] - 7)/9], Print[n]], {n, 3, 1000, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

PARI

for(k=1,oo,ispseudoprime(10^k\9*7-5*10^(k\2))&&print1(k",")) \\ M. F. Hasler, Feb 08 2020

Formula

a(n) = 2*A183178(n+1) + 1.

Extensions

Name corrected by Jon E. Schoenfield, Oct 31 2018