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 A107127 Numbers n such that (10^(2n+1)+54*10^n-1)/9 is prime. 45
 0, 3, 33, 311, 2933, 22235, 39165, 41585 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). a(9) > 10^5. - Robert Price, Apr 30 2017 REFERENCES C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9. LINKS Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's) Makoto Kamada, Prime numbers of the form 11...11711...11 FORMULA a(n) = (A077789(n)-1)/2. EXAMPLE 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. MATHEMATICA Do[If[PrimeQ[(10^(2n + 1) + 54*10^n - 1)/9], Print[n]], {n, 3250}] PROG (PARI) for(n=0, 1e4, if(ispseudoprime(t=(10^(2*n+1)+54*10^n)\9), print1(t", "))) \\ Charles R Greathouse IV, Jul 15 2011 CROSSREFS Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187. Sequence in context: A180416 A043038 A274264 * A207323 A135697 A226508 Adjacent sequences:  A107124 A107125 A107126 * A107128 A107129 A107130 KEYWORD nonn,more,base AUTHOR Farideh Firoozbakht, May 19 2005 EXTENSIONS Edited by Ray Chandler, Dec 28 2010 a(6)-a(8) from Robert Price, Apr 30 2017 STATUS approved

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Last modified February 18 04:48 EST 2020. Contains 332011 sequences. (Running on oeis4.)