OFFSET
1,1
LINKS
Antti Karttunen, Table of n, a(n) for n = 1..10000
N. S. Dattani & N. Bryans, Quantum factorization of 56153 with only 4 qubits, arXiv:1411.6758 [quant-ph], 2014.
EXAMPLE
291311 = 523 * 557 is included (as term a(334)) because 523 ("1000001011" in binary) and 557 ("1000101101" in binary) differ in exactly three bit-positions.
MATHEMATICA
Select[Range@ 30000, And[Length@ # == 2, IntegerLength[#1, 2] == IntegerLength[#2, 2] & @@ #, Total@ BitXor[IntegerDigits[#1, 2], IntegerDigits[#2, 2]] == 3 & @@ #] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #] &] (* Michael De Vlieger, Oct 08 2016 *)
PROG
(PARI)
A000523 = n -> logint(n, 2);
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
isA261075(n) = { my(a, b); if(bigomega(n)!=2, 0, a = A020639(n); b = (n/a); ((A000523(a) == A000523(b)) && (3 == norml2(binary(bitxor(a, b)))))); };
i=0; n=0; while(i < 10000, n++; if(isA261075(n), i++; write("b261075.txt", i, " ", n)));
(Scheme, with Antti Karttunen's IntSeq-library)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Sep 22 2015
STATUS
approved