A107126 Numbers n such that (10^(2n+1)+45*10^n-1)/9 is prime.

10, 14, 40, 59, 160, 412, 560, 1289, 1846

Offset

1,1

Comments

n is in the sequence iff the palindromic number 1(n).6.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m + 1, 16m + 2, 16m + 5, 22m + 1, 22m + 9, etc. (the proof is easy).

a(10) > 10^5. - Robert Price, Sep 28 2015

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..9.

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

Makoto Kamada, Prime numbers of the form 11...11611...11

Index entries for primes involving repunits.

Formula

a(n) = (A077787(n)-1)/2.

Example

14 is in the sequence because (10^(2*14+1)+45*10^14-1)/9=1(14).6.1(14) = 11111111111111611111111111111 is prime.

Mathematica

Do[If[PrimeQ[(10^(2n + 1) + 45*10^n - 1)/9], Print[n]], {n, 2500}]
Position[Table[FromDigits[Join[PadRight[{}, n, 1], {6}, PadRight[{}, n, 1]]], {n, 1850}], _?PrimeQ]//Flatten (* Harvey P. Dale, Jun 22 2017 *)

Prog

(PARI) is(n)=ispseudoprime((10^(2*n+1)+45*10^n-1)/9) \\ Charles R Greathouse IV, Jun 06 2017

Crossrefs

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

Sequence in context: A144967 A328635 A260564 * A247091 A025122 A173684

Adjacent sequences: A107123 A107124 A107125 * A107127 A107128 A107129

Keyword

nonn,base

Author

Farideh Firoozbakht, May 19 2005

Extensions

Edited by Ray Chandler, Dec 28 2010

Status

approved