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A261073
Semiprimes whose prime factors are of equal binary length and which differ from each other in one bit position only.
7
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
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. also A261074, A261075.
Cf. A071697 (a subsequence).
Intersection of A085721 and A261077.
Sequence in context: A093989 A357037 A356460 * A261080 A356494 A291595
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Sep 22 2015
STATUS
approved