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 A101462 Smallest k such that 2^k-prime(n) is prime. 0

%I #5 Mar 31 2012 10:23:47

%S 2,3,3,39,4,4,6,5,6,5,7,11,6,29,6,6,6,6,7,10,9,9,8,8,7,26,9,8,7,10,47,

%T 14,10,9,12,31,15,9,8,8,12,9,14,21,10,9,25,261,8,9,8,8,9,8,14,10,16,9,

%U 15,10,9,12,11,14,9,12,9,791,10,9,16,20,15,9,11,10,16,15,26,9,12,11,10

%N Smallest k such that 2^k-prime(n) is prime.

%C Conjecture: sequence is defined for all n. First unproved n: 286 Prime(286)=1871, up to date, tested up to k=40959, none 2^k-Prime(286) is prime.

%C Primo was used for testing large primes.

%H Lei Zhou, <a href="http://www.bme.emory.edu/~lzhou/prime/">Between 2^n and primes</a>.

%e Prime(1)=2, 2^2-2 = 2 is prime

%e Prime(2)=3, 2^3-3 = 5 is prime

%e ...

%e Prime(68)=337, 2^791-337 is prime.

%t f[n_] := Block[{p = Prime@ n}, k = Ceiling@ Log2@ p; While[! PrimeQ[2^k - p], k++]; k]; Array[f, 83]

%Y Cf. A094076.

%K nonn

%O 1,1

%A _Lei Zhou_, Jan 20 2005

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Last modified September 15 10:23 EDT 2024. Contains 375932 sequences. (Running on oeis4.)