cp's OEIS Frontend

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

%I A101462 #5 Mar 31 2012 10:23:47
%S A101462 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 A101462 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 A101462 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 A101462 Smallest k such that 2^k-prime(n) is prime.
%C A101462 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 A101462 Primo was used for testing large primes.
%H A101462 Lei Zhou, <a href="http://www.bme.emory.edu/~lzhou/prime/">Between 2^n and primes</a>.
%e A101462 Prime(1)=2, 2^2-2 = 2 is prime
%e A101462 Prime(2)=3, 2^3-3 = 5 is prime
%e A101462 ...
%e A101462 Prime(68)=337, 2^791-337 is prime.
%t A101462  f[n_] := Block[{p = Prime@ n}, k = Ceiling@ Log2@ p; While[! PrimeQ[2^k - p], k++]; k]; Array[f, 83]
%Y A101462 Cf. A094076.
%K A101462 nonn
%O A101462 1,1
%A A101462 _Lei Zhou_, Jan 20 2005