A040026 If n=r*2^s, r odd, then a(n)=t*r, where t is smallest (in magnitude) number such that 1=t*r+u*2^s.

1, 1, 3, 1, 5, 3, 7, 1, 9, 5, 11, -3, 13, 7, 15, 1, 17, 9, 19, 5, 21, 11, 23, 9, 25, 13, 27, -7, 29, 15, 31, 1, 33, 17, 35, 9, 37, 19, 39, -15, 41, 21, 43, -11, 45, 23, 47, -15, 49, 25, 51, 13, 53, 27, 55, -7, 57, 29, 59, -15, 61, 31, 63, 1, 65, 33, 67, 17, 69, 35, 71, 9, 73, 37, 75, -19

Offset

1,3

References

J. Neukirch, Class Field Theory, Springer, p. 1.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

24=3*2^3, 1=3*3-1*2^3, a(24)=3*3=9.

Mathematica

a[1] = a[2] = 1; a[n_?OddQ] := n; a[n_] := (s = IntegerExponent[n, 2]; r = n/2^s; eq = Reduce[1 == t*r + u*2^s, {t, u}, Integers] /. C[_] -> 0; t*r /. Solve[eq] // First ); Table[a[n], {n, 1, 76}] (* Jean-François Alcover, Jun 07 2013 *)

Prog

(C) for(n=1; n<=100; n++) { r=n; s=1; while((r&1)==0) { r>>=1; s<<=1; } for(t=1; t<9999; t++) { if(((t*r-1)%s)==0) { printf("%d, ", t*r); break; } if(((t*r+1)%s)==0) { printf("%d, ", -t*r); break; } } if((n%10)==0) printf("\n"); if(t==9999) exit(0); //"not found": error }
(Haskell)
a040026 n = f 1 where
   f t | (1 - t*r) `mod` s == 0 = t*r
       | (1 + t*r) `mod` s == 0 = - t*r
       | otherwise              = f (t + 1)
   (r, s) = split n 1
   split x y | m == 0 = split x' (2 * y)
             | m == 1 = (x, y) where (x', m) = divMod x 2
-- Reinhard Zumkeller, Jul 21 2012

Crossrefs

|a(n)| differs from A000265, as a(24)=9.

Sequence in context: A000265 A227140 A106617 * A106609 A171968 A093474

Adjacent sequences: A040023 A040024 A040025 * A040027 A040028 A040029

Keyword

sign,easy,nice,look

Author

N. J. A. Sloane

Extensions

More terms from Arlin Anderson (starship1(AT)gmail.com)

Status

approved