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

6, 35, 323, 437, 713, 899, 1763, 1961, 2021, 2537, 3233, 4757, 5561, 5609, 6497, 7313, 9797, 10403, 10961, 11009, 18209, 19043, 21353, 22499, 23393, 26969, 27221, 29177, 37001, 38021, 39203, 45113, 71273, 72899, 79523, 87953, 95477, 98201, 99221, 106793, 114857, 114929, 123353

Offset

1,1

Links

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

Example

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.
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.

Mathematica

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 *)

Prog

(PARI)
A000523 = n -> logint(n, 2);
A020639(n) = if(1==n, n, vecmin(factor(n)[, 1]));
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)))))); };
i=0; n=0; while(i < 5000, n++; if(isA261073(n), i++; write("b261073.txt", i, " ", n)));
(Scheme, with Antti Karttunen's IntSeq-library)
(define A261073 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (= (A000523 (A020639 n)) (A000523 (A006530 n))) (= 1 (A101080bi (A020639 n) (A006530 n)))))))

Crossrefs

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

Cf. also A261074, A261075.

Cf. A071697 (a subsequence).

Intersection of A085721 and A261077.

Sequence in context: A093989 A357037 A356460 * A261080 A356494 A291595

Adjacent sequences: A261070 A261071 A261072 * A261074 A261075 A261076

Keyword

nonn,base

Author

Antti Karttunen, Sep 22 2015

Status

approved