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A107123
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Numbers n such that (10^(2n+1)+18*10^n-1)/9 is prime.
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44
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OFFSET
| 1,3
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COMMENTS
| n is in the sequence iff the palindromic number 1(n).3.1(n) is prime (dot between numbers means concatenation). If n is a positive term of the sequence then n is not of the forms 3m, 6m+4, 12m+10, 28m+5, 28m+8, etc. (the proof is easy). 11 divides each palindromic number of the form 1(n).2.1(n) so there is no prime of this form.
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REFERENCES
| C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
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LINKS
| Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 11...11311...11
Index entries for primes involving repunits.
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FORMULA
| a(n) = (A077789(n)-1)/2.
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EXAMPLE
| 19 is in the sequence because the palindromic number (10^(2*19+1)+18*10^19-1)/9 = 1(19).3.1(19) = 111111111111111111131111111111111111111 is prime.
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MATHEMATICA
| Do[If[PrimeQ[(10^(2n + 1) + 18*10^n - 1)/9], Print[n]], {n, 2500}]
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PROG
| (PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2n+1)+18*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
| Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.
Sequence in context: A056005 A034572 A041393 * A193047 A055875 A089659
Adjacent sequences: A107120 A107121 A107122 * A107124 A107125 A107126
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KEYWORD
| nonn
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AUTHOR
| Farideh Firoozbakht (mymontain(AT)yahoo.com), May 19 2005
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EXTENSIONS
| Edited by Ray Chandler (rayjchandler(AT)sbcglobal.net), Dec 28 2010
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