A261075 Semiprimes whose prime factors are of equal binary length and which differ from each other in exactly three bit positions.

527, 551, 1591, 2173, 2491, 2623, 3127, 5183, 5963, 6059, 6557, 6767, 6887, 7031, 7373, 7571, 7597, 7739, 7979, 8051, 8249, 8549, 8633, 8881, 9017, 9523, 9701, 10541, 10807, 11303, 11639, 12091, 12317, 12827, 14351, 19519, 20413, 20989, 21823, 22331, 23213, 24047, 24613, 24881, 24883, 25777, 25807, 26549, 26671, 26827, 26989, 27661, 28199, 28459, 28757, 29329

Offset: 1

Author

Antti Karttunen, Sep 22 2015

Keywords

• nonn
• base

Examples

			291311 = 523 * 557 is included (as term a(334)) because 523 ("1000001011" in binary) and 557 ("1000101101" in binary) differ in exactly three bit-positions.
		

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.

Crossrefs

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

Cf. also A261073, A261074.

Subsequence of A085721.

Programs

Mathematica

Select[Range@ 30000, And[Length@ # == 2, IntegerLength[#1, 2] == IntegerLength[#2, 2] & @@ #, Total@ BitXor[IntegerDigits[#1, 2], IntegerDigits[#2, 2]] == 3 & @@ #] &@ Flatten@ Map[ConstantArray[#1, #2] & @@ # &, FactorInteger@ #] &] (* Michael De Vlieger, Oct 08 2016 *)

PARI

A000523 = n -> logint(n, 2);
A020639(n) = if(1==n,n,vecmin(factor(n)[, 1]));
isA261075(n) = { my(a,b); if(bigomega(n)!=2, 0, a = A020639(n); b = (n/a); ((A000523(a) == A000523(b)) && (3 == norml2(binary(bitxor(a,b)))))); };
i=0; n=0; while(i < 10000, n++; if(isA261075(n), i++; write("b261075.txt", i, " ", n)));

Scheme

;; With Antti Karttunen's IntSeq-library.
(define A261075 (MATCHING-POS 1 1 (lambda (n) (and (= 2 (A001222 n)) (= (A000523 (A020639 n)) (A000523 (A006530 n))) (= 3 (A101080bi (A020639 n) (A006530 n)))))))