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Search: id:A107127
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| A107127 |
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Numbers n such that (10^(2n+1)+54*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).7.1(n) is prime (dot between numbers means concatenation). If n is in the sequence then n is not of the forms 3m+1, 6m, 6m+2, 7m+2, 16m+9, 16m+14, 18m+1, 18m+7, 22m+13, 22m+19, 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...11711...11
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FORMULA
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a(n) = (A077789(n)-1)/2.
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EXAMPLE
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3 is in the sequence because (10^(2*3+1)+54*10^3-1)/9=1(3).7.1(3)=1117111 is prime.
2933 is in the sequence because (10^(2*2933+1)+54*10^2933-1)/9=1(2933).7.1(2933) is prime.
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MATHEMATICA
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Do[If[PrimeQ[(10^(2n + 1) + 54*10^n - 1)/9], Print[n]], {n, 3250}]
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CROSSREFS
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Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A114633-A114647.
Sequence in context: A132122 A003129 A043038 this_sequence A135697 A097486 A121515
Adjacent sequences: A107124 A107125 A107126 this_sequence A107128 A107129 A107130
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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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