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

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

Offset: 1

Author

Farideh Firoozbakht, May 19 2005

Keywords

• nonn
• base
• more

Comments

k is in the sequence iff the palindromic number 1(k).5.1(k) is prime (dot between numbers means concatenation). If k is in the sequence then k 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

Examples

			1248 is in the sequence because (10^(2*1248+1)+36*10^1248-1)/9=1(1248).5.1(1248) 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 11...11511...11
• Index entries for primes involving repunits.

Crossrefs

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

Programs

Magma

[n: n in [0..700] | IsPrime((10^(2*n+1)+36*10^n-1) div 9)]; // Vincenzo Librandi, Oct 13 2015

Mathematica

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

PARI

is(n)=ispseudoprime((10^(2*n+1)+36*10^n-1)/9) \\ Charles R Greathouse IV, Jun 06 2017

Formula

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

Extensions

Edited by Ray Chandler, Dec 28 2010

a(12) from Robert Price, Oct 12 2015

a(13) from Robert Price, Sep 05 2023