cp's OEIS Frontend

A261073 Semiprimes whose prime factors are of equal binary length and which differ from each other in one bit position only.

%I A261073 #22 Feb 22 2025 20:05:17
%S A261073 6,35,323,437,713,899,1763,1961,2021,2537,3233,4757,5561,5609,6497,
%T A261073 7313,9797,10403,10961,11009,18209,19043,21353,22499,23393,26969,
%U A261073 27221,29177,37001,38021,39203,45113,71273,72899,79523,87953,95477,98201,99221,106793,114857,114929,123353
%N A261073 Semiprimes whose prime factors are of equal binary length and which differ from each other in one bit position only.
%H A261073 Antti Karttunen, <a href="/A261073/b261073.txt">Table of n, a(n) for n = 1..5000</a>
%e A261073 6 = 2*3 is present, as 2 in binary is "10" and 3 in binary is "11", so both have two (significant) bits and they differ only in one bit-position from each other.
%e A261073 35 = 5*7 is present, as 5 in binary is "101" and 7 in binary is "111", which both have three bits, differing only in the middle position from each other.
%t A261073 Select[Range[10^6], And[Length@ # == 2, IntegerLength[#1, 2] == IntegerLength[#2, 2] & @@ #, Total@ BitXor[IntegerDigits[#1, 2], IntegerDigits[#2, 2]] == 1 & @@ #] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #] &] (* _Michael De Vlieger_, Oct 08 2016 *)
%o A261073 (PARI)
%o A261073 A000523 = n -> logint(n, 2);
%o A261073 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A261073 isA261073(n) = { my(a,b); if(bigomega(n)!=2, 0, a=A020639(n); b = (n/a); ((A000523(a) == A000523(b)) && (1 == norml2(binary(bitxor(a,b)))))); };
%o A261073 i=0; n=0; while(i < 5000, n++; if(isA261073(n), i++; write("b261073.txt", i, " ", n)));
%o A261073 (Scheme)
%o A261073 ;; With _Antti Karttunen_'s IntSeq-library.
%o A261073 (define A261073 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (= (A000523 (A020639 n)) (A000523 (A006530 n))) (= 1 (A101080bi (A020639 n) (A006530 n)))))))
%Y A261073 Cf. A000523, A001222, A006530, A020639, A101080.
%Y A261073 Cf. also A261074, A261075.
%Y A261073 Cf. A071697 (a subsequence).
%Y A261073 Intersection of A085721 and A261077.
%K A261073 nonn,base
%O A261073 1,1
%A A261073 _Antti Karttunen_, Sep 22 2015