A205791 -id:A205791 - cp's OEIS frontend

A344308 Numbers k such that A205791(k) = k+1.

1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 23, 26, 29, 30, 34, 35, 37, 38, 39, 42, 43, 46, 47, 51, 53, 57, 58, 59, 65, 67, 69, 70, 73, 74, 78, 79, 83, 85, 86, 87, 89, 91, 94, 95, 97, 102, 103, 105, 106, 107, 109, 111, 113, 114, 115, 118, 119, 127, 129, 130, 133, 134, 137, 138, 139, 141, 145

Offset: 1

Robert Israel, May 14 2021

nonn

			a(6) = 7 is a term because A205791(7) = 8.

Robert Israel, Table of n, a(n) for n = 1..1258

Cf. A205791.

Subset of A005117.

N:= 200: # for terms <= 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:
select(t -> V[t] = t+1, [$1..N]);

Select[Range@200,(k=1;While[FreeQ[Mod[Table[k^5-j^5,{j,k-1}],#],0],k++];k)==#+1&] (* Giorgos Kalogeropoulos, May 14 2021 *)

A205792 Least positive integer j such that n divides k^5-j^5, where k, as in A205791, is the least number for which there is such a j.

Original entry on oeis.org

1, 1, 1, 2, 1, 1, 1, 2, 3, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 1, 2, 1, 1, 1, 6, 1, 1, 1, 2, 3, 1, 1, 1, 3, 1, 1, 2, 7, 1, 1, 2, 1, 3, 2, 2, 1, 1, 1, 2, 2, 2, 3, 2, 1, 2, 1, 2, 1, 1, 3, 6, 1, 1, 1, 2, 5, 1, 1, 2, 3, 3, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 1, 7, 3

Offset: 1

Clark Kimberling, Feb 01 2012

nonn

For a guide to related sequences, see A204892.

			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

Cf. A204892.

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 *)

cp's OEIS Frontend

A344308 Numbers k such that A205791(k) = k+1.

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