A277129 Largest m < n such that 2^m == 2^n (mod n).

0, 1, 1, 3, 1, 4, 4, 7, 3, 6, 1, 10, 1, 11, 11, 15, 9, 12, 1, 16, 15, 12, 12, 22, 5, 14, 9, 25, 1, 26, 26, 31, 23, 26, 23, 30, 1, 20, 27, 36, 21, 36, 29, 34, 33, 35, 24, 46, 28, 30, 43, 40, 1, 36, 35, 53, 39, 30, 1, 56, 1, 57, 57, 63, 53, 56, 1, 60, 47, 58, 36, 66, 64, 38, 55, 58, 47, 66, 40, 76, 27, 62, 1

Offset

1,4

Comments

If n is odd, then a(n) = n - A002326((n-1)/2).

Links

Table of n, a(n) for n=1..83.

Mathematica

Table[m = n - 1; While[Mod[2^m, n] != Mod[2^n, n], m--]; m, {n, 83}] (* Michael De Vlieger, Oct 02 2016 *)

Prog

(PARI) a(n) = {if(n==0, return(0)); my(pt = valuation(n, 2), odd = n/2^pt, ul = odd-A002326(odd\2)); forstep(i = n-1, ul, -1, if(Mod(2, n)^i==Mod(2, n)^n, return(i)))} \\ David A. Corneth, Oct 01 2016
A002326(n)=if(n<0, 0, znorder(Mod(2, 2*n+1)))

Crossrefs

Cf. A002326, A015910, A270096.

Sequence in context: A117374 A202142 A021322 * A036412 A363569 A200027

Adjacent sequences: A277126 A277127 A277128 * A277130 A277131 A277132

Keyword

nonn

Author

Thomas Ordowski, Oct 01 2016

Extensions

More terms from Altug Alkan, Oct 01 2016

Status

approved