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 A253242 Least k>=0 such that n^(2^k)+1 is prime (for even n), or (n^(2^k)+1)/2 is prime (for odd n); -1 if no such k exists. 1
 0, 0, 0, 0, 0, 2, -1, 0, 0, 1, 0, 0, 1, 1, 0, 2, 0, 1, 1, 0, 0, 2, 1, 0, 1, -1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,6 COMMENTS Least k such that the generalized Fermat number in base n (GFN(k,n)) is prime. a(n) = -1 if n is in A070265 (perfect powers with an odd exponent). a(n) is currently unknown for n = {31, 38, 50, 55, 62, 63, 67, 68, 77, 83, 86, 89, 91, 92, 97, 98, 99, 104, 107, 109, 122, 123, 127, 135, 137, ...} Corresponding primes are {3, 2, 5, 3, 7, 1201, 0, 5, 11, 61, 13, 7, 197, 113, 17, 41761, 19, 181, 401, 11, 23, 139921, 577, 13, 677, 0, 29, 421, 31, ...}. (use 0 if a(n) = -1) All 2 <= n <= 1500 and 0 <= k <= 14 are checked, the first occurrence of k (start with k = 0) in a(n) are {2, 11, 7, 43, 41, 75, 274, 234, 331, 1342, 824, ...}. LINKS Chris Caldwell, Generalized Fermat number Richard Fischer, List of generalized Fermat primes in odd bases Yves Gallot, Generalized Fermat prime search Wilfrid Keller, Factorization of GFN(n,2) Wilfrid Keller, Factorization of GFN(n,3) Wilfrid Keller, Factorization of GFN(n,5) Wilfrid Keller, Factorization of GFN(n,6) Wilfrid Keller, Factorization of GFN(n,10) Wilfrid Keller, Factorization of GFN(n,12) Jeppe Stig Salling Nielsen, List of generalized Fermat primes in even bases up to 1000 MathWorld, Generalized Fermat number OEIS wiki, Generalized Fermat number Wikipedia, Generalized Fermat number FORMULA a(2n) = A228101(n) = log_2(A079706(n)). a(A006093(n)) = 0, a(A076274(n)) = 0, a(A070265(n)) = -1. EXAMPLE a(7) = 2 since (7^(2^0)+1)/2 and (7^(2^1)+1)/2 are not primes, but (7^(2^2)+1)/2 = 1201 is prime. a(14) = 1 since 14^(2^0)+1 is not prime, but 14^(2^1)+1 = 197 is prime. MATHEMATICA Table[k=0; While[p=If[EvenQ[n], (2n)^(2^k)+1, ((2n)^(2^k)+1)/2]; k<12 && !PrimeQ[p], k=k+1]; If[k==12, -1, k], {n, 2, 1500}] PROG (PARI) f(n) = for(k=0, 11, if(ispseudoprime(n^(2^k)+1), return(k))); -1 g(n) = for(k=0, 11, if(ispseudoprime((n^(2^k)+1)/2), return(k))); -1 a(n) = if(n%2==0, f(n), g(n)) (PARI) f(n, k)=if(n%2, (n^(2^k)+1)/2, n^(2^k)+1) a(n)=if(ispower(-n), -1, my(k); while(!ispseudoprime(f(n, k)), k++); k) \\ Charles R Greathouse IV, Apr 20 2015 CROSSREFS Cf. A079706, A228101, A084712, A123669, A058064, A057856, A130536, A080121, A077659, A122900. Sequence in context: A086017 A000161 A060398 * A260649 A122855 A140727 Adjacent sequences:  A253239 A253240 A253241 * A253243 A253244 A253245 KEYWORD sign,more,hard,changed AUTHOR Eric Chen, Apr 19 2015 STATUS approved

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Last modified September 19 02:54 EDT 2020. Contains 337175 sequences. (Running on oeis4.)