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A293424 Hamming distance between two consecutive semiprimes. 1
1, 4, 2, 1, 1, 3, 2, 4, 2, 5, 2, 1, 2, 1, 2, 5, 1, 1, 3, 2, 1, 7, 1, 4, 3, 5, 3, 2, 1, 2, 2, 2, 1, 4, 2, 3, 2, 1, 3, 2, 1, 6, 1, 2, 3, 2, 1, 4, 2, 2, 2, 1, 5, 3, 4, 2, 2, 2, 3, 1, 5, 3, 2, 1, 2, 2, 5, 1, 2, 1, 3, 2, 1, 2, 6, 2, 2, 3, 3, 1, 2, 8, 2, 4, 1, 3, 1, 2, 5, 1, 1, 3, 1, 2, 2, 1, 4, 1, 4, 2, 6, 1, 2, 1, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The least semiprime whose Hamming distance between it and its successor semiprime is k: 4, 9, 15, 6, 26, 123, 62, 254, 511, 3071, 2047, 8189, 32765, 16382, 98303, 65531, 393215, 262142, 1572863, 2621438, 1048574, 16777207, 8388607, 50331647, 33554429, 134217721, 268435451, etc.

Not surprisingly, the above are often the largest semiprime < 2^j.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

a(1) = 1 because the semiprimes 4 & 6, 100_2 & 110_2 have a Hamming distance of 1;

a(2) = 4 because the semiprimes 6 & 9, 110_2 & 1001_2 have a Hamming distance of 4;

a(3) = 2 because the semiprimes 9 & 10, 1001_2 & 1010_2 have a Hamming distance of 2; etc.

MAPLE

semiprimes:= select(t -> numtheory:-bigomega(t)=2, [$4..1023]):

L:=map(t -> convert(t+1024, base, 2), semiprimes):

map(t -> 11 - numboccur(0, t), L[2..-1]-L[1..-2]); # Robert Israel, Oct 08 2017

# alternative

read("transforms") :

A293424 := proc(n)

    local s1, s2 ;

    s1 := A001358(n) ;

    s2 := A001358(n+1) ;

    XORnos(s1, s2) ;

    wt(%) ;

end proc: # R. J. Mathar, Jan 06 2018

MATHEMATICA

Count[ IntegerDigits[ BitXor[ #[[1]], #[[2]]], 2], 1] & /@ Partition[ Select[ Range@330, PrimeOmega@# == 2 &], 2, 1]

PROG

(PARI) lista(nn) = my(v = select(x->bigomega(x)==2, vector(nn, k, k))); vector(#v-1, k, norml2(binary(bitxor(v[k], v[k+1])))); \\ Michel Marcus, Oct 11 2017

CROSSREFS

Cf. A001358 (semiprimes), A205510 (between consecutive primes).

Sequence in context: A036466 A097526 A051149 * A152145 A288251 A051758

Adjacent sequences:  A293421 A293422 A293423 * A293425 A293426 A293427

KEYWORD

base,nonn

AUTHOR

Robert G. Wilson v, Oct 08 2017

STATUS

approved

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)