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

1,2

Links

Table of n, a(n) for n=1..30.

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 *)

Prog

(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++)
(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

Crossrefs

Cf. A068869, A240937.

Sequence in context: A176602 A322194 A174120 * A016739 A158452 A208929

Adjacent sequences: A240936 A240937 A240938 * A240940 A240941 A240942

Keyword

nonn

Author

Derek Orr, Aug 03 2014

Extensions

a(18) onward from Robert G. Wilson v, Aug 04 2014

Status

approved