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 A182116 Carmichael numbers that only have composite XOR couples as defined in A182108. 3
 410041, 19384289, 41341321, 43620409, 69331969, 93030145, 122785741, 130032865, 133344793, 133800661, 157731841, 238527745, 334783585, 396262945, 403043257, 413631505, 417241045, 477726145, 490503601, 561777121, 631071001, 686059921, 707926801, 854197345 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS There are 255 Carmichael numbers below 10^8 but only 6 of them have this property. LINKS Jon E. Schoenfield, Table of n, a(n) for n = 1..427 PROG (Magma) XOR := func; 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; function Korselt(X, n); i:=1; while IsDefined(X, i) do b:=(n-1)mod(X[i]-1); if (b ne 0) then return false; else i:=i+1; end if; end while; return true; end function; function IsCarmichael(n); if IsPrime(n) then return false; end if; A:=AssociativeArray(); if IsSquarefree(n) then A:=PrimeDivisors(n); if Korselt(A, n) then return true; else return false; end if; else return false; end if; end function; for i:=561 to 100000001 by 2 do if IsCarmichael(i) then if IsClardynum(i, Ilog2(i)) then i; end if; end if; end for; CROSSREFS Cf. A002997, A182108. Sequence in context: A295445 A183705 A233995 * A249405 A237676 A307475 Adjacent sequences: A182113 A182114 A182115 * A182117 A182118 A182119 KEYWORD nonn AUTHOR Brad Clardy, Apr 12 2012 EXTENSIONS a(11)-a(19) by Brad Clardy, May 10 2014 More terms and b-file (using the Magma program by Brad Clardy and the b-file of Carmichael numbers from A002997) from Jon E. Schoenfield, May 10 2014 STATUS approved

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Last modified November 29 06:17 EST 2023. Contains 367422 sequences. (Running on oeis4.)