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URL: https://oeis.org/A303744

⇱ A303744 - OEIS

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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
OFFSET
1,2
COMMENTS
Apart from 1 and 4, all terms == 2 (mod 4). - Robert Israel, Jun 25 2018
LINKS
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
KEYWORD
nonn
AUTHOR
Adam Kertesz, Apr 29 2018
STATUS
approved