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A107125 Numbers n such that (10^(2n+1) + 36*10^n - 1)/9 is prime. 2
0, 1, 7, 45, 115, 681, 1248, 2481, 2689, 6198, 13197, 60126 (list; graph; refs; listen; history; text; internal format)
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(13) > 10^5. - Robert Price, Oct 12 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..12.

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

STATUS

approved

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Last modified September 23 21:14 EDT 2017. Contains 292391 sequences.