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.

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, 97, 89, 109, 113, 103, 113, 89, 137, 1, 157, 181, 239, 139, 241, 139, 179, 233, 193, 163, 241, 173, 283, 167, 271, 193, 277, 181, 179, 199, 1, 193, 223, 239, 239, 233, 751

Offset

1,1

Comments

Note that a(1) = 3 and a(2) = 4 use -2 as the preceding prime. - Robert Israel, Nov 18 2015

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Example

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.

Maple

f:= proc(n) local m;
    m:= ilcm($1..n);
    if m < 3 then m + 2
    else  m - prevprime(m)
    fi
end proc:
A000961:= select(t -> nops(numtheory:-factorset(t))<=1, [$1..1000]):
map(f, A000961); # Robert Israel, Nov 18 2015

Prog

(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

Crossrefs

Cf. A000961, A003418, A051451.

Sequence in context: A176979 A370319 A299989 * A215202 A139344 A137925

Adjacent sequences: A058019 A058020 A058021 * A058023 A058024 A058025

Keyword

nonn

Author

Labos Elemer, Nov 15 2000

Status

approved