A303744 Numbers that are not a difference between same powers (greater than 1) of positive numbers.

1, 2, 4, 6, 10, 14, 18, 22, 30, 34, 38, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 82, 86, 90, 94, 102, 106, 110, 114, 118, 122, 126, 130, 134, 138, 142, 146, 150, 154, 158, 162, 166, 170, 174, 178, 182, 186, 190, 194, 198, 202, 206, 210, 214, 222, 226, 230, 234, 238, 246, 250, 254, 258, 262, 266, 270, 274, 278, 282, 286, 290

Offset

1,2

Comments

Apart from 1 and 4, all terms == 2 (mod 4). - Robert Israel, Jun 25 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

Odd numbers greater than 1 are differences of squares, so they are not here.
8 is not a term, 9 - 1: difference of two squares;
26 is not a term, 27 - 1: difference of two cubes.

Maple

N:= 1000: # to get all terms <= N
S:= {1, 2, 4, seq(i, i=6..N, 4)}:
for p from 3 to ilog2(N+1) do
  for n from 1 while n^p - (n-1)^p <= N do
    if n^p > N then m0:= ceil((n^p - N)^(1/p)) else m0:= 1 fi;
    for m from m0 to n-1 do
      v:= n^p-m^p;
      S:= S minus {v};
    od
od od:
sort(convert(S, list)); # Robert Israel, Jun 25 2018

Crossrefs

Sequences of numbers that are difference of powers: A024352 (squares), A181123 (cubes).

And of further n-th powers: A147857 (4th), A181124 (5th), A181125 (6th), A181126 (7th), A181127 (8th), A181128 (9th).

Sequence in context: A062091 A100143 A234941 * A362488 A059254 A024518

Adjacent sequences: A303741 A303742 A303743 * A303745 A303746 A303747

Keyword

nonn

Author

Adam Kertesz, Apr 29 2018

Status

approved