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 A191474 Smallest prime q such that q + prime(n) is a power of 2. 2

%I #28 Sep 01 2023 21:17:27

%S 2,5,3,549755813881,5,3,47,13,41,3,97,2011,23,536870869,17,11,5,3,61,

%T 953,439,433,173,167,31,67108763,409,149,19,911,140737488355201,16253,

%U 887,373,107,2147483497,32611,349,89,83,3917,331,16193,2096959,59,313,33554221

%N Smallest prime q such that q + prime(n) is a power of 2.

%C Corresponding exponents of 2: 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, 1, 9, 8, 7, 10, 47, 14, 10, 9, 8, 31, 15, 9, 8, 8, 12, 9, 14, 21, 8, 9, 1, ...

%H Robert Israel, <a href="/A191474/b191474.txt">Table of n, a(n) for n = 1..285</a>

%e 2 + 2 = 2^2,

%e 3 + 5 = 2^3,

%e 5 + 3 = 2^3,

%e 7 + 549755813881 = 2^39,

%e 11 + 5 = 2^4.

%p f:= proc(n) local p,m,t,q;

%p p:= ithprime(n);

%p for t from ilog2(p) do

%p q:= 2^t - p;

%p if isprime(q) then return q fi;

%p od;

%p end proc:

%p map(f, [\$1..50]); # _Robert Israel_, Dec 23 2020

%t f[p_] := NestWhile[2 # &, 2^Ceiling[Log[2, p]], ! PrimeQ[# - p] &] - p;

%t f /@ Prime@Range@47 (* _David Trimas_, Jul 30 2023 *)

%K nonn

%O 1,1

%A _Zak Seidov_, Aug 28 2012

%E a(26) corrected by _Robert Israel_, Dec 23 2020

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Last modified September 13 22:05 EDT 2024. Contains 375910 sequences. (Running on oeis4.)