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Search: id:A107124
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| A107124 |
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Numbers n such that (10^(2n+1)+27*10^n-1)/9 is prime. |
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2
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OFFSET
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1,1
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COMMENT
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n is in the sequence iff the palindromic number 1(n).4.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 16m+11, 16m+12, 18m+11, 18m+15, 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)
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Factorizations of 11...11411...11
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FORMULA
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a(n) = (A077780(n)-1)/2.
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EXAMPLE
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32 is in the sequence because the palindromic number (10^(2*32+1)+27*10^32-1)/9 = 1(32).4.1(32) =
11111111111111111111111111111111411111111111111111111111111111111 is prime.
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MATHEMATICA
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Do[If[PrimeQ[(10^(2n + 1) + 27*10^n - 1)/9], Print[n]], {n, 2200}]
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CROSSREFS
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Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A114633-A114647.
Sequence in context: A032815 A041053 A103108 this_sequence A141049 A052830 A041895
Adjacent sequences: A107121 A107122 A107123 this_sequence A107125 A107126 A107127
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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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