A107649 Numbers n such that (10^(2n+1)+72*10^n-1)/9 is prime.

1, 4, 26, 187, 226, 874, 13309, 34016, 42589

Offset

1,2

Comments

n is in the sequence iff the palindromic number 1(n).9.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m+5, 22m+3, 22m+7, etc. (the proof is easy).

a(10) > 123528. - Robert Price, Sep 28 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..9.

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

Makoto Kamada, Prime numbers of the form 11...11911...11

Index entries for primes involving repunits.

Formula

a(n) = (A077795(n)-1)/2.

Example

26 is in the sequence because (10^(2*26+1)+72*10^26-1)/9=1(26).9.1(26)
= 11111111111111111111111111911111111111111111111111111 is prime.

Mathematica

Do[If[PrimeQ[(10^(2n + 1) + 72*10^n - 1)/9], Print[n]], {n, 3000}]
prQ[n_]:=Module[{c=PadRight[{}, n, 1]}, PrimeQ[FromDigits[Join[c, {9}, c]]]]; Select[Range[13500], prQ] (* Harvey P. Dale, Jan 19 2014 *)

Prog

(PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+72*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011

Crossrefs

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

Sequence in context: A264226 A052775 A137964 * A371517 A052763 A213101

Adjacent sequences: A107646 A107647 A107648 * A107650 A107651 A107652

Keyword

nonn,more,base

Author

Farideh Firoozbakht, May 19 2005

Extensions

Edited by Ray Chandler, Dec 28 2010

a(8)-a(9) from Robert Price, Sep 28 2017

Status

approved