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A261077 Semiprimes whose prime factors differ from each other in one bit position only.

%I A261077 #13 Feb 22 2025 20:05:42
%S A261077 6,21,33,35,57,65,161,185,201,323,377,393,437,473,497,713,899,1529,
%T A261077 1577,1763,1769,1841,1961,2021,2537,3233,3473,3497,3737,4553,4601,
%U A261077 4757,5561,5609,5753,6497,7217,7313,9593,9797,10265,10403,10841,10961,11009,12297,14129,15689,17513,18209,19043,19337,21353,22499,23129,23393,26969,27221,27233,29177
%N A261077 Semiprimes whose prime factors differ from each other in one bit position only.
%H A261077 Antti Karttunen, <a href="/A261077/b261077.txt">Table of n, a(n) for n = 1..5000</a>
%e A261077 21 = 3*7 is present because 3 in binary is "11" ("011" when extended with a leading zero) and 7 in binary is "111", and these differ only in the bit-position 2 (with indexing where the least significant bit is in the position 0).
%e A261077 33 = 3*11 is present because 3 in binary is "11" ("0011" when extended with two leading zeros) and 11 in binary is "1011", and these differ only in the bit-position 3.
%o A261077 (PARI)
%o A261077 A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
%o A261077 isA261077 = n -> if(bigomega(n)!=2, 0, (1 == norml2(binary(bitxor((n/A020639(n)),A020639(n))))));
%o A261077 i=0; n=0; while(i < 5000, n++; if(isA261077(n), i++; write("b261077.txt", i, " ", n)));
%o A261077 (Scheme)
%o A261077 ;; With _Antti Karttunen_'s IntSeq-library.
%o A261077 (define A261077 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (= 1 (A101080bi (A020639 n) (A006530 n)))))))
%Y A261077 Cf. A000523, A001222, A006530, A020639, A101080.
%Y A261077 Cf. also A261073, A261080 (subsequences).
%Y A261077 Subsequence of A261078.
%Y A261077 Gives the positions of ones in A260737.
%K A261077 nonn,base
%O A261077 1,1
%A A261077 _Antti Karttunen_, Sep 22 2015