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Search: id:A107649
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| A107649 |
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Numbers n such that (10^(2n+1)+72*10^n-1)/9 is prime. |
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29
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OFFSET
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1,2
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COMMENT
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n is in the sequence iff the palindromic number 1(n).9.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m, 6m+5, 22m+3, 22m+7, etc. (the proof is easy).
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REFERENCES
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C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.
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LINKS
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Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Factorizations of 11...11911...11
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FORMULA
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a(n) = (A077795(n)-1)/2.
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EXAMPLE
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26 is in the sequence because (10^(2*26+1)+72*10^26-1)/9=1(26).9.1(26)
= 11111111111111111111111111911111111111111111111111111 is prime.
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MATHEMATICA
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Do[If[PrimeQ[(10^(2n + 1) + 72*10^n - 1)/9], Print[n]], {n, 3000}]
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CROSSREFS
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Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A114633-A114647.
Sequence in context: A098443 A052775 A137964 this_sequence A052763 A084211 A114496
Adjacent sequences: A107646 A107647 A107648 this_sequence A107650 A107651 A107652
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KEYWORD
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nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), May 19 2005
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