Search: id:A023057
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%I A023057
%S A023057 6,14,22,29,31,34,42,44,46,50,52,54,58,62,64,66,70,72,78,82,84,86,88,90,
%T A023057 91,96,98,102,105,110,111,114,117,118,120,122,124,126,130,132,134,136,
%U A023057 140,142,153,156,158,160,162,164,165,172,176,177,178,179,181,182,188,190
%N A023057 (Apparently) not the difference between adjacent perfect powers (A001597, 
               integers of form a^b, a >= 1, b >= 2).
%C A023057 Catalan's conjecture (now a theorem) is that 1 occurs just once as a 
               difference, between 8 and 9.
%D A023057 G. Everest, A. van der Poorten, I. Shparlinski and T. Ward, Recurrence 
               Sequences, Amer. Math. Soc., 2003; see esp. p. 255.
%H A023057 Alf van der Poorten, <a href="a023057.txt">Remarks on the sequence of 
               'perfect' powers</a>
%t A023057 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]] 
               (from Robert G. Wilson v)
%Y A023057 Cf. A001597 (perfect powers), A023055 (complement). See also A074980, 
               A074981, A077286.
%Y A023057 Sequence in context: A110223 A125086 A138290 this_sequence A062316 A079299 
               A043445
%Y A023057 Adjacent sequences: A023054 A023055 A023056 this_sequence A023058 A023059 
               A023060
%K A023057 nonn,nice
%O A023057 1,1
%A A023057 David W. Wilson (davidwwilson(AT)comcast.net)

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