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Search: id:A131457
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| A131457 |
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Higgs' semiprimes: a(n+1) = next semiprime such that a(n+1)-1 | (a(1)...a(n))^2. |
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1
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| 4, 9, 10, 21, 22, 25, 26, 33, 34, 35, 46, 49, 51, 55, 57, 58, 65, 69, 77, 82, 85, 86, 87, 91, 93, 94, 95, 106, 111, 115, 118, 119, 121, 122, 123, 129, 133, 134, 141, 142, 143, 145, 146, 155, 161, 166, 169, 177, 178, 183, 185, 187, 201, 202, 203, 205, 206, 209, 213
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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This is to semiprimes A001358 as A007459 is to primes A000040. Finite or infinite?
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FORMULA
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a(n+1) = MIN{j in A001358 such that (j-1) | PRODUCT[i=1..n]a(i)^2.
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EXAMPLE
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a(1) = 4 because 4 = 2^2 is the first semiprime.
a(2) = 9 because 9 = 3^2 is the next semiprime after 4, where 9-1=8 divides 4^2 = 16.
a(3) = 10 because 10 = 2*5 is the next semiprime after 9 where 10-9=9 divides (4*9)^2.
a(4) = 21 because 21 = 3*7 is the next semiprime after 10, where 10-1=9 divides (4*9*10)^2.
a(5) = 22 because 22 = 2*11 is the next semiprime after 21, where 21-1=20 divides (4*9*10*21)^2.
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MAPLE
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isA001358 := proc(n) if numtheory[bigomega](n) = 2 then true ; else false; fi ; end: A131457 := proc(n) option remember ; local a, prevpr; if n =1 then 4; else prevpr := (mul(A131457(i), i=1..n-1))^2 ; a := A131457(n-1)+1 ; while not isA001358(a) or prevpr mod (a-1) <> 0 do a := a+1 ; od; RETURN(a) ; fi ; end: seq(A131457(n), n=1..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2007
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CROSSREFS
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Cf. A000040, A001358, A007459, A070552, A109373.
Sequence in context: A119718 A051884 A131368 this_sequence A072525 A107621 A098144
Adjacent sequences: A131454 A131455 A131456 this_sequence A131458 A131459 A131460
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Oct 21 2007
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EXTENSIONS
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Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2007
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