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A261074 Semiprimes whose prime factors are of equal binary length and which differ from each other in exactly two bit positions. 5
143, 391, 493, 589, 667, 1517, 1739, 1927, 2257, 2419, 2501, 2773, 2867, 3599, 4891, 5293, 5767, 5893, 6499, 6901, 7081, 7169, 7171, 7387, 7811, 7957, 8137, 8453, 8611, 9379, 9991, 10033, 10057, 10379, 10573, 11021, 11227, 11413, 11663, 13081, 13589, 13843, 17947, 19781, 21509, 21877, 22657, 23449, 23701, 23707, 25217, 25283, 26069, 26441, 27029 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

N. S. Dattani & N.  Bryans, Quantum factorization of 56153 with only 4 qubits, arXiv:1411.6758 [quant-ph], 2014.

EXAMPLE

143 = 11*13 is included because 11 ("1011" in binary) and 13 ("1101" in binary) differ from each other in exactly two bit-positions.

56153 = 233 * 241 is included (as term a(119)) because 233 ("11101001" in binary) and 241 ("11110001" in binary) differ from each other in exactly two bit-positions.

MATHEMATICA

Select[Range[10^5], And[Length@ # == 2, IntegerLength[#1, 2] == IntegerLength[#2, 2] & @@ #, Total@ BitXor[IntegerDigits[#1, 2], IntegerDigits[#2, 2]] == 2 & @@ #] &@ 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]));

isA261074(n) = { my(a, b); if(bigomega(n)!=2, 0, a = A020639(n); b = (n/a); ((A000523(a) == A000523(b)) && (2 == norml2(binary(bitxor(a, b)))))); };

i=0; n=0; while(i < 10000, n++; if(isA261074(n), i++; write("b261074.txt", i, " ", n)));

(Scheme, with Antti Karttunen's IntSeq-library)

(define A261074 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (= (A000523 (A020639 n)) (A000523 (A006530 n))) (= 2 (A101080bi (A020639 n) (A006530 n)))))))

CROSSREFS

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

Cf. also A261073, A261075.

Subsequence of A085721.

Sequence in context: A158136 A153874 A003902 * A213337 A156963 A126703

Adjacent sequences:  A261071 A261072 A261073 * A261075 A261076 A261077

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Sep 22 2015

STATUS

approved

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Last modified November 20 12:37 EST 2018. Contains 317402 sequences. (Running on oeis4.)