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 A125954 Least number k > 0 such that ((2n+1)^k - 2^k)/(2n-1) is prime. 2
 2, 2, 3, 2, 2, 3, 2, 2, 11, 2, 5, 11, 2, 2, 5, 71, 2, 3, 2, 2, 167, 2, 17, 3, 2, 197, 149, 2, 2, 3, 3, 2, 2267, 2, 2, 3, 3, 2, 29, 2, 2531, 167, 2, 7, 3, 3, 2, 61, 2, 2, 11, 2, 2, 157, 2, 5, 7, 7, 149, 3, 5, 2, 379, 2, 41, 3, 2, 2, 3, 79, 11, 3, 2, 2, 97, 3, 2, 3, 3, 2, 1321, 2, 17, 31, 2, 61 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS All terms are primes. a(n) = 2 for n = {1,2,4,5,7,8,10,13,14,17,19,20,22,...} = A067076 Numbers n such that 2n+3 is a prime. a(34),...,a(40) = {2,2,3,3,2,29,2}. a(42),...,a(80) = {167,2,7,3,3,2,61,2,2,11,2,2,157,2,5,7,7,149,3,5,2,379,2,41,3,2,2,3,79,11,3,2,2,97,3,2,3,3,2}. a(82),...,a(90) = {2,17,31,2,61,7,2,2,5}. a(93),...,a(95) = {383,2,2}. a(97),...,a(100) = {2,2,5,7}. a(102),...,a(124) = {13,11,2,5,5,17,3,103,2,19,2,2,3,2,31,37,2,2,3,3,7,3,2}. a(127),...,a(131) = {2,61,31,2,157}. a(133),...,a(142) = {2,2,7,3,2,13,2,2,7,3}. a(144),...,a(146) = {173,2,11}. a(148),...,a(150) = {3,17,107}. a(n) is currently unknown for n = {33,41,81,91,92,96,101,125,126,132,143,147,...}. LINKS MATHEMATICA Do[k = 1; While[ !PrimeQ[((2n+1)^k - 2^k)/(2n-1)], k++ ]; Print[k], {n, 100}] (* Ryan Propper, Mar 29 2007 *) lnk[n_]:=Module[{k=1}, While[!PrimeQ[((2n+1)^k-2^k)/(2n-1)], k++]; k]; Array[ lnk, 90] (* Harvey P. Dale, May 19 2012 *) CROSSREFS Cf. A067076. Cf. A000043 = Primes p such that 2^p - 1 is prime. Cf. A001348 = Mersenne numbers: 2^p - 1, where p is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A125958 = Least number k > 0 such that (2^k + (2n-1)^k)/(2n+1) is prime. Sequence in context: A046027 A283671 A046028 * A122443 A262945 A270516 Adjacent sequences:  A125951 A125952 A125953 * A125955 A125956 A125957 KEYWORD hard,nonn AUTHOR Alexander Adamchuk, Feb 07 2007 EXTENSIONS More terms from Ryan Propper, Mar 29 2007 STATUS approved

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Last modified June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)