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 A254522 Numerators of (2^n - 1 + (-1)^n)/(2*n), n > 0. 1
 0, 1, 1, 2, 3, 16, 9, 16, 85, 256, 93, 512, 315, 4096, 5461, 2048, 3855, 65536, 13797, 131072, 349525, 1048576, 182361, 1048576, 3355443, 16777216, 22369621, 33554432, 9256395, 268435456, 34636833, 67108864, 1431655765, 4294967296, 17179869183, 8589934592, 1857283155, 68719476736, 91625968981 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS An autosequence of the first kind is a sequence which main diagonal is A000004. Difference table of a(n)/A093803(n): 0, 1, 1, 2, 3, 16/3, ... 1, 0, 1, 1, 7/3, 11/3, ... -1, 1, 0, 4/3, 4/3, 10/3, ... 2, -1, 4/3, 0, 2, 2, ... -3, 7/3, -4/3, 2, 0, 16/5, ... 16/3, -11/3, 10/3, -2, 16/5, 0, ... etc. This is an autosequence of the first kind. Its first (or second) upper diagonal is A075101(n)/(2*A000265(n)). From Robert Israel, Apr 03 2017: (Start) If p is a prime == 5 (mod 8), then a(5*p) = (2^(5*p-1)-1)/5 and a(5*p+3) = 2^(5*p) = 10*a(5*p)+2. This explains pairs such as a(25) = 3355443 a(28) = 33554432 and a(65) = 3689348814741910323 a(68) = 36893488147419103232. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..3321 MAPLE seq(numer((2^n-1+(-1)^n)/(2*n)), n=1..50); # Robert Israel, Feb 01 2015 MATHEMATICA Table[Numerator[(2^n - 1 + (-1)^n)/(2*n)], {n, 39}] (* Michael De Vlieger, Feb 01 2015 *) CROSSREFS Cf. A000004, A075101, A093803, A099430. Sequence in context: A066841 A266211 A074270 * A007120 A092973 A126007 Adjacent sequences: A254519 A254520 A254521 * A254523 A254524 A254525 KEYWORD nonn AUTHOR Paul Curtz, Jan 31 2015 EXTENSIONS a(25) corrected by Robert Israel, Apr 03 2017 STATUS approved

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Last modified December 8 08:56 EST 2022. Contains 358693 sequences. (Running on oeis4.)