A205791 Least positive integer k such that n divides k^5-j^5 for some j in [1,k-1].
2, 3, 4, 4, 6, 7, 8, 4, 6, 11, 3, 8, 14, 15, 16, 4, 18, 9, 20, 12, 22, 3, 24, 8, 6, 27, 6, 16, 30, 31, 2, 4, 4, 35, 36, 12, 38, 39, 40, 12, 7, 43, 44, 5, 18, 47, 48, 8, 14, 11, 52, 28, 54, 9, 7, 16, 58, 59, 60, 32, 7, 4, 24, 6, 66, 8, 68, 36, 70, 71, 4, 12, 74, 75, 16, 40
Offset: 1
Examples
1 divides 2^5-1^5 -> k=2, j=1 2 divides 3^5-1^5 -> k=3, j=1 3 divides 4^5-1^5 -> k=4, j=1 4 divides 4^5-2^5 -> k=4, j=2 5 divides 6^5-1^5 -> k=6, j=1 6 divides 7^5-1^5 -> k=7, j=1
Links
- Robert Israel, Table of n, a(n) for n = 1..3000
Programs
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Maple
N:= 100: # for a(1)..a(N) V:= Vector(N): count:= 0: for k from 1 while count < N do for j from 1 to k-1 while count < N do Q:= select(t -> t <= N and V[t] = 0, numtheory:-divisors(k^5-j^5)); if Q <> {} then newcount:= nops(Q); count:= count + newcount; V[convert(Q,list)]:= k; fi od od: convert(V,list); # Robert Israel, May 14 2021 -
Mathematica
s = Table[n^4, {n, 1, 120}] ; lk = Table[ NestWhile[# + 1 &, 1, Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1, Length[s]}] Table[NestWhile[# + 1 &, 1, Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &], {j, 1, Length[lk]}] (* Peter J. C. Moses, Jan 27 2012 *) Array[(k=1;While[FreeQ[Mod[Table[k^5-j^5,{j,k-1}],#],0],k++];k)&,100] (* Giorgos Kalogeropoulos, May 14 2021 *)
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