A117430 - OEIS

%I #21 Jul 23 2020 05:02:48

%S 3,-1,0,-2,1,2,-2,-2,-2,-3,2,2,-2,-4,4,2,-8,-6,-2,-3,-2,-2,4,2,-6,-2,

%T 4,2,-3,17,9,-4,-8,-6,12,14,-2,-6,-8,-2,-6,24,-2,14,-6,-4,-18,-6,-3,

%U -6,16,-10,16,-12,12,-2,16,6,16,-12,-2,-6,12,-12,-8,-19,-6,6,24,-16,4,2,16,-4,-8,-4,16

%N Integer k such that 5^n + k = A117429(n).

%C (+/-) distance from 5^n to the nearest semiprime.

%C a(0)=3 and a(1)=-1 are the only terms == 3 (mod 4), as 5^n + 3 is divisible by 4. - _Robert Israel_, May 03 2018

%H Robert Israel, <a href="/A117430/b117430.txt">Table of n, a(n) for n = 0..111</a>

%F a(n) = Integer k such that 5^n + k = A117429(n). a(n) = A117429(n) - 5^n. a(n) = Min{k such that A001358(i) + k = 5^n}.

%e a(0) = 3 because 5^0 + 3 = 4 = A001358(1) and no semiprime is closer to 5^0.

%e a(1) = -1 because 5^1 - 1 = 4 = A001358(1) and no semiprime is closer to 5^1.

%e a(2) = 0 because 5^2 + 0 = 25 = A001358(9), no semiprime is closer to 5^2 [this is the only 0 element].

%e a(3) = -2 because 5^3 - 2 = 123 = 3 * 41 = A001358(42), no semiprime is closer.

%e a(4) = 1 because 5^4 + 1 = 626 = 2 * 313, no semiprime is closer.

%e a(5) = 2 because 5^5 + 2 = 3127 = 53 * 59, no semiprime is closer.

%p nsp:= proc(n) uses numtheory; local k;

%p   if bigomega(n)=2 then return n fi;

%p   for k from 1 do

%p     if n-k > 0 and bigomega(n-k)=2 then return n-k fi;

%p     if bigomega(n+k)=2 then return n+k fi

%p   od

%p end proc:

%p seq(nsp(5^n)-5^n, n=0..30); # _Robert Israel_, May 03 2018

%t nsp[n_] := Module[{k}, If[PrimeOmega[n] == 2, Return[n]]; For[k = 1, True, k++, If[n-k > 0 && PrimeOmega[n-k] == 2, Return[n-k]]; If[PrimeOmega[n+k] == 2, Return[n+k]]]];

%t a[n_] := a[n] = nsp[5^n] - 5^n;

%t Table[Print[n, " ", a[n]]; a[n], {n, 0, 76}] (* _Jean-François Alcover_, Jul 23 2020, after Maple *)

%Y Cf. A000079, A001358, A117387, A117405, A117406, A117416, A117429.

%K sign

%O 0,1

%A _Jonathan Vos Post_, Mar 14 2006

%E More terms from _Robert Israel_, May 03 2018