A107125 Numbers n such that (10^(2n+1) + 36*10^n - 1)/9 is prime.

0, 1, 7, 45, 115, 681, 1248, 2481, 2689, 6198, 13197, 60126, 100072

Offset

1,3

Comments

n is in the sequence iff the palindromic number 1(n).5.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+2, 18m+12, 18m+14, 22m+4, 22m+6, etc. (the proof is easy).

a(14) > 100233. - _Robert Price, Sep 05 2023

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..13.

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

Makoto Kamada, Prime numbers of the form 11...11511...11

Index entries for primes involving repunits.

Formula

a(n) = (A077783(n)-1)/2.

Example

1248 is in the sequence because (10^(2*1248+1)+36*10^1248-1)/9=1(1248).5.1(1248) is prime.

Mathematica

Do[If[PrimeQ[(10^(2n + 1) + 36*10^n - 1)/9], Print[n]], {n, 2200}]

Prog

(Magma) [n: n in [0..700] | IsPrime((10^(2*n+1)+36*10^n-1) div 9)]; // Vincenzo Librandi, Oct 13 2015
(PARI) is(n)=ispseudoprime((10^(2*n+1)+36*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: A171493 A262772 A153492 * A212105 A208826 A206808

Adjacent sequences: A107122 A107123 A107124 * A107126 A107127 A107128

Keyword

nonn,base,more

Author

Farideh Firoozbakht, May 19 2005

Extensions

Edited by Ray Chandler, Dec 28 2010

a(12) from Robert Price, Oct 12 2015

a(13) from Robert Price, Sep 05 2023

Status

approved