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A303744 Numbers that are not a difference between same powers (greater than 1) of positive numbers. 2
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 (list; graph; refs; listen; history; text; internal format)
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 * A059254 A024518 A128422

Adjacent sequences:  A303741 A303742 A303743 * A303745 A303746 A303747

KEYWORD

nonn

AUTHOR

Adam Kertesz, Apr 29 2018

STATUS

approved

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Last modified April 21 07:24 EDT 2021. Contains 343146 sequences. (Running on oeis4.)