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

6, 21, 33, 35, 57, 65, 161, 185, 201, 323, 377, 393, 437, 473, 497, 713, 899, 1529, 1577, 1763, 1769, 1841, 1961, 2021, 2537, 3233, 3473, 3497, 3737, 4553, 4601, 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

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..5000

Example

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).
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.

Prog

(PARI)
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
isA261077 = n -> if(bigomega(n)!=2, 0, (1 == norml2(binary(bitxor((n/A020639(n)), A020639(n))))));
i=0; n=0; while(i < 5000, n++; if(isA261077(n), i++; write("b261077.txt", i, " ", n)));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A261077 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (= 1 (A101080bi (A020639 n) (A006530 n)))))))

Crossrefs

Cf. A000523, A001222, A006530, A020639, A101080.

Cf. also A261073, A261080 (subsequences).

Subsequence of A261078.

Gives the positions of ones in A260737.

Sequence in context: A302868 A064440 A106634 * A063126 A256866 A115702

Adjacent sequences: A261074 A261075 A261076 * A261078 A261079 A261080

Keyword

nonn,base

Author

Antti Karttunen, Sep 22 2015

Status

approved