A124276 Terms k of A068563 such that k/2 is not a term of A068563.

1, 6, 18, 20, 42, 54, 60, 100, 126, 136, 156, 162, 180, 220, 294, 300, 342, 378, 408, 420, 468, 486, 500, 540, 620, 660, 680, 780, 820, 882, 900, 1026, 1092, 1100, 1134, 1224, 1260, 1314, 1332, 1404, 1458, 1500, 1620, 1806, 1860, 1980, 2028, 2040, 2058, 2100

Offset: 1

Author

Alexander Adamchuk, Oct 23 2006

Keywords

• nonn

Comments

A068563 are the numbers n such that 2^n (mod n) = 4^n (mod n). If k is in the sequence A068563 then 2k is also in the sequence A068563, but if 2m is in the sequence A068563 m is not necessarily a term of the sequence A068563.

Examples

			A068563 begins 1, 2, 4, 6, 8, 12, 16, 18, 20, 24, 32, 36, 40, 42, ... .
Thus a(0) = 1, a(1) = 6, a(2) = 18, a(3) = 20, a(4) = 42 because 1/2, 3, 9, 10, 21 are not the terms of A068563.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A068563.

Programs

Maple

a:= proc(n) option remember; local k;
      for k from `if`(n=1, 1, a(n-1)+1)
      while (2&^k mod k <> 4&^k mod k) or
         (irem(k, 2, 'r')=0 and (2&^r mod r = 4&^r mod r))
      do od; k
    end:
seq(a(n), n=1..50);  # Alois P. Heinz, May 16 2013

Mathematica

Prepend[Select[Range[2, 2100], (PowerMod[2, #, #] == PowerMod[4, #, #]) && ! (PowerMod[2, #/2, #/2] == PowerMod[4, #/2, #/2]) &], 1]