cp's OEIS Frontend

A261075 Semiprimes whose prime factors are of equal binary length and which differ from each other in exactly three bit positions.

%I A261075 #16 Feb 22 2025 20:05:34
%S A261075 527,551,1591,2173,2491,2623,3127,5183,5963,6059,6557,6767,6887,7031,
%T A261075 7373,7571,7597,7739,7979,8051,8249,8549,8633,8881,9017,9523,9701,
%U A261075 10541,10807,11303,11639,12091,12317,12827,14351,19519,20413,20989,21823,22331,23213,24047,24613,24881,24883,25777,25807,26549,26671,26827,26989,27661,28199,28459,28757,29329
%N A261075 Semiprimes whose prime factors are of equal binary length and which differ from each other in exactly three bit positions.
%H A261075 Antti Karttunen, <a href="/A261075/b261075.txt">Table of n, a(n) for n = 1..10000</a>
%H A261075 N. S. Dattani & N.  Bryans, <a href="http://arxiv.org/abs/1411.6758">Quantum factorization of 56153 with only 4 qubits</a>, arXiv:1411.6758 [quant-ph], 2014.
%e A261075 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.
%t A261075 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 *)
%o A261075 (PARI)
%o A261075 A000523 = n -> logint(n, 2);
%o A261075 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A261075 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)))))); };
%o A261075 i=0; n=0; while(i < 10000, n++; if(isA261075(n), i++; write("b261075.txt", i, " ", n)));
%o A261075 (Scheme)
%o A261075 ;; With _Antti Karttunen_'s IntSeq-library.
%o A261075 (define A261075 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (= (A000523 (A020639 n)) (A000523 (A006530 n))) (= 3 (A101080bi (A020639 n) (A006530 n)))))))
%Y A261075 Cf. A000523, A001222, A006530, A020639, A101080.
%Y A261075 Cf. also A261073, A261074.
%Y A261075 Subsequence of A085721.
%K A261075 nonn,base
%O A261075 1,1
%A A261075 _Antti Karttunen_, Sep 22 2015