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 A201914 Least prime p such that p+1 is divisible by 2^n and not by 2^(n+1). 3
 2, 5, 3, 7, 47, 31, 191, 127, 1279, 3583, 5119, 6143, 20479, 8191, 81919, 294911, 1114111, 131071, 786431, 524287, 17825791, 14680063, 138412031, 109051903, 654311423, 1912602623, 738197503, 2818572287, 7247757311, 3758096383, 228707008511, 2147483647 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS See A126717 for the least k such that k*2^n-1 is prime. For every n >= 1 there are infinitely many prime numbers p such that p + 1 is divisible by 2^n and not by 2^(n + 1). - Marius A. Burtea, Mar 10 2020 REFERENCES Laurențiu Panaitopol, Alexandru Gica, Arithmetic problems and number theory, Ed. Gil, Zalău, (2006), ch. 13, p. 78, pr. 5 (in Romanian). LINKS Donovan Johnson, Table of n, a(n) for n = 0..1000 MATHEMATICA Table[k = 1; While[p = k*2^n - 1; ! PrimeQ[p], k = k + 2]; p, {n, 0, 40}] PROG (MAGMA) a:=[]; for n in [0..31] do k:=1; while not IsPrime(k*2^n-1) do k:=k+2; end while; Append(~a, k*2^n-1); end for; a; // Marius A. Burtea, Mar 10 2020 CROSSREFS Cf. A008864 (primes + 1), A057775 (p-1 case), A126717. For n>0, sequence is first term of A002144, A007520, A141194, A142041, A142939, ... Sequence in context: A249162 A134563 A192178 * A331217 A021398 A186631 Adjacent sequences:  A201911 A201912 A201913 * A201915 A201916 A201917 KEYWORD nonn AUTHOR T. D. Noe, Dec 27 2011 STATUS approved

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Last modified July 31 06:57 EDT 2021. Contains 346369 sequences. (Running on oeis4.)