cp's OEIS Frontend

A058022 Difference between lcm(1,..,n) and the largest prime before lcm(1,..,n) where n runs over the prime powers A000961, LCMs are in A051451.

%I A058022 #15 Nov 20 2015 11:41:11
%S A058022 3,4,1,1,1,1,1,17,19,23,17,43,1,1,29,41,1,43,1,43,47,83,1,83,61,149,1,
%T A058022 97,89,109,113,103,113,89,137,1,157,181,239,139,241,139,179,233,193,
%U A058022 163,241,173,283,167,271,193,277,181,179,199,1,193,223,239,239,233,751
%N A058022 Difference between lcm(1,..,n) and the largest prime before lcm(1,..,n) where n runs over the prime powers A000961, LCMs are in A051451.
%C A058022 Note that a(1) = 3 and a(2) = 4 use -2 as the preceding prime. - _Robert Israel_, Nov 18 2015
%H A058022 Charles R Greathouse IV, <a href="/A058022/b058022.txt">Table of n, a(n) for n = 1..1000</a>
%e A058022 6th and 7th different values of LCM-s are 840 and 2520. Deviation of immediate preceding primes(839,2503) are:1 and 17. For n=1 LCM[1]=1 and prime=-2 is the largest with deviation 3. So the sequence starts with 3.
%p A058022 f:= proc(n) local m;
%p A058022     m:= ilcm($1..n);
%p A058022     if m < 3 then m + 2
%p A058022     else  m - prevprime(m)
%p A058022     fi
%p A058022 end proc:
%p A058022 A000961:= select(t -> nops(numtheory:-factorset(t))<=1, [$1..1000]):
%p A058022 map(f, A000961); # _Robert Israel_, Nov 18 2015
%o A058022 (PARI) N=2; print1("3, 4"); for(n=3,1e3, if(isprimepower(n,&p), N*=p; print1(", "N-precprime(N-1)))) \\ _Charles R Greathouse IV_, Nov 18 2015
%Y A058022 Cf. A000961, A003418, A051451.
%K A058022 nonn
%O A058022 1,1
%A A058022 _Labos Elemer_, Nov 15 2000