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A107125
Numbers n such that (10^(2n+1) + 36*10^n - 1)/9 is prime.
3
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.
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
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