A240939 Least number k >= 0 such that n! + k is a perfect power.
0, 2, 2, 1, 1, 9, 1, 81, 729, 225, 324, 39169, 82944, 176400, 215296, 3444736, 26167684, 114349225, 255004929, 1158920361, 11638526761, 42128246889, 191052974116, 97216010329, 2430400258225, 1553580508516, 4666092737476, 565986718738441, 2137864362693921, 5112360635841936
Offset: 1
Keywords
Links
- Robert Israel, Table of n, a(n) for n = 1..805
Programs
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Maple
f:= proc(n) local v,m,p,r; m:= infinity; v:= n!; p:= 1; do p:= nextprime(p); if 2^p >= m+v then break fi; r:= ceil(v^(1/p))^p - v; if r < m then m:= r fi; od; m end proc: map(f, [$1..50]); -
Mathematica
nextPerfectPower[n_] := Min@ Table[(Floor[n^(1/k)] + 1)^k, {k, 2, 1 + Floor@ Log2@ n}]; f[n_] := nextPerfectPower[n!] - n!; f[1] = 0; Array[f, 30] (* Robert G. Wilson v, Aug 04 2014 *) -
PARI
a(n)=for(k=0,10^10,s=n!+k;if(ispower(s)||s==1,return(k))) n=1;while(n<50,print1(a(n),", ");n++)
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PARI
a(n)=for(k=1,n!,if(2^k>n!,kk=k;break));if(kk==1,return(0));L=List([]);for(i=2,kk,listinsert(L,ceil(n!^(1/i))^i-n!,1));listsort(L);L[1] vector(40, n, a(n)) \\ faster program
Extensions
a(18) onward from Robert G. Wilson v, Aug 04 2014
Comments