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A182108 Odd composite numbers in successive intervals [2^i +1 .. 2^(i+1) -1] i=1,2,3... such that there are only composite symmetric XOR couples in either the original interval or any recursively halved interval that contains them. 3
513, 695, 925, 1177, 1355, 1395, 1507, 1681, 1685, 1687, 1689, 1819, 1827, 1893, 1959, 2043, 2165, 2169, 2637, 2651, 2757, 2875, 2987, 3159, 3339, 3417, 3503, 3649, 3681, 3743, 3873, 3963, 3975, 4041, 4169, 4353, 4489, 4767, 4773, 4805, 4845, 4881, 5123 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The description of the process is outlined in A199824. Up to the interval that starts 2^10 there are only 109 of these numbers, while there are a mere 50 primes of the type in A199824.
LINKS
PROG
(Magma)
XOR := func<a, b | Seqint([ (adigs[i] + bdigs[i]) mod 2 : i in [1..n]], 2)
where adigs := Intseq(a, 2, n)
where bdigs := Intseq(b, 2, n)
where n := 1 + Ilog2(Max([a, b, 1]))>;
function IsClardynum(X, i)
if i eq 1 then
return true;
else
xornum:=2^i - 2;
xorcouple:=XOR(X, xornum);
if (IsPrime(xorcouple)) then
return false;
else
return IsClardynum(X, i-1);
end if;
end if;
end function;
for i:= 3 to 10001 by 2 do
if not IsPrime(i) then
if IsClardynum(i, Ilog2(i)) then i;
end if;
end if;
end for;
CROSSREFS
Cf. A199824.
Sequence in context: A087931 A044879 A060947 * A066697 A076338 A237620
KEYWORD
nonn
AUTHOR
Brad Clardy, Apr 12 2012
STATUS
approved

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Last modified February 23 13:26 EST 2024. Contains 370283 sequences. (Running on oeis4.)