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a(n) is the least prime p such that p+prime(n) has exactly n prime factors, counted with multiplicity.
1

%I #46 Mar 10 2020 23:32:20

%S 3,3,3,17,37,83,271,557,1129,2531,2017,21467,28631,24533,73681,98251,

%T 196549,589763,524221,2621369,5242807,14155697,69205933,16777127,

%U 83885983,67108763,1543503769,1006632853,1342177171,3623878543,11811159937,54358179709,32212254583,225485782901,260919263083

%N a(n) is the least prime p such that p+prime(n) has exactly n prime factors, counted with multiplicity.

%H Robert Israel, <a href="/A332860/b332860.txt">Table of n, a(n) for n = 1..400</a>

%F A001222(a(n)+A000040(n)) = n.

%e a(4) = 17 because 17 is prime and 17 + prime(4) = 17 + 7 = 24 = 2^3*3 has 4 prime factors counted with multiplicity, and no smaller prime works.

%p g:= proc(n, N, pmax)

%p local Res, k, p;

%p if n = 0 then return [[]] fi;

%p Res:= NULL;

%p p:=1;

%p do

%p p:= nextprime(p);

%p if p >= pmax or 2^(n-1)*p > N then return [Res] fi;

%p for k from 1 to n while 2^(n-k)*p^k <= N do

%p Res:= Res, op(map(t -> [op(t),p\$k], procname(n-k,N/p^k,p)));

%p od;

%p od;

%p end proc:

%p h:= (n,N) -> sort(map(convert,g(n,N,N/2^(n-1)+1),`*`)):

%p f:= proc(n) local pn, N, lastN, R, r;

%p pn:= ithprime(n);

%p N:= 2^n-1;

%p do

%p lastN:= N;

%p N:= 2*N;

%p R:= select(`>`,h(n,N), lastN);

%p for r in R do if r > pn and isprime(r-pn) then return r-pn fi od;

%p od;

%p end proc:

%p map(f, [\$1..50]);

%Y Cf. A000040, A001222.

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Mar 10 2020

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Last modified September 20 09:27 EDT 2024. Contains 376068 sequences. (Running on oeis4.)