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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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45
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OFFSET
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1,2
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COMMENTS
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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).
a(10) > 123528. - Robert Price, Sep 28 2017
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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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Table of n, a(n) for n=1..9.
Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 11...11911...11
Index entries for primes involving repunits.
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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}]
prQ[n_]:=Module[{c=PadRight[{}, n, 1]}, PrimeQ[FromDigits[Join[c, {9}, c]]]]; Select[Range[13500], prQ] (* Harvey P. Dale, Jan 19 2014 *)
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PROG
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(PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+72*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011
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CROSSREFS
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Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.
Sequence in context: A264226 A052775 A137964 * A052763 A213101 A084211
Adjacent sequences: A107646 A107647 A107648 * A107650 A107651 A107652
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KEYWORD
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nonn,more,base
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AUTHOR
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Farideh Firoozbakht, May 19 2005
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EXTENSIONS
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Edited by Ray Chandler, Dec 28 2010
a(8)-a(9) from Robert Price, Sep 28 2017
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STATUS
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approved
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