|
%I #17 Sep 04 2023 23:15:42
%S 6,14,22,29,31,34,42,44,46,50,52,54,58,62,64,66,70,72,78,82,84,86,88,
%T 90,91,96,98,102,105,110,111,114,117,118,120,122,124,126,130,132,134,
%U 136,140,142,153,156,158,160,162,164,165,172,176,177,178,179,181,182,188,190
%N (Apparently) not the difference between adjacent perfect powers (A001597, integers of form a^b, a >= 1, b >= 2).
%C Catalan's conjecture (now a theorem) is that 1 occurs just once as a difference, between 8 and 9.
%D G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%H Robert G. Wilson v, <a href="/A023057/b023057.txt">Table of n, a(n) for n = 1..4479</a>
%H Alf van der Poorten, <a href="/A023057/a023057.txt">Remarks on the sequence of 'perfect' powers</a>.
%t pp = Union[ Join[{1}, Flatten[ Table[n^i, {n, 2, Sqrt[10^12]}, {i, 2, Log[n, 10^12]}]]]]; l = Length[pp]; d = Sort[Take[pp, -l + 1] - Take[pp, l - 1]]; Complement[ Table[i, {i, 1, 200}], Take[ Union[d], 200]] (* _Robert G. Wilson v_ *)
%Y Cf. A001597 (perfect powers), A023055 (complement). See also A074980, A074981, A077286.
%K nonn,nice
%O 1,1
%A _David W. Wilson_
|
