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 A261075 Semiprimes whose prime factors are of equal binary length and which differ from each other in exactly three bit positions. 5
 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 (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 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. 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 *) PROG (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))))))) CROSSREFS Cf. A000523, A001222, A006530, A020639, A101080. Cf. also A261073, A261074. Subsequence of A085721. Sequence in context: A093226 A153660 A337779 * A250754 A158364 A232885 Adjacent sequences: A261072 A261073 A261074 * A261076 A261077 A261078 KEYWORD nonn,base AUTHOR Antti Karttunen, Sep 22 2015 STATUS approved

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Last modified September 11 17:54 EDT 2024. Contains 375839 sequences. (Running on oeis4.)