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Search: id:A037074
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| A037074 |
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Products of twin primes. |
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+0
43
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| 15, 35, 143, 323, 899, 1763, 3599, 5183, 10403, 11663, 19043, 22499, 32399, 36863, 39203, 51983, 57599, 72899, 79523, 97343, 121103, 176399, 186623, 213443, 272483, 324899, 359999, 381923, 412163, 435599, 656099, 675683, 685583, 736163
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Except for the first term, all entries have digital root 8. - Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 11 2004
Albert A. Mullin states that m is a product of twin primes iff phi(m)*sigma(m) = (m-3)*(m+1), where phi(m) = A000010(m) and sigma(m) = A000203(m). Of course, for a product of distinct primes p*q we know sigma(p*q) = (p+1)*(q+1), and if p, q, are twin primes, say q = p + 2, then sigma(p*q) = (p+1)*(q+1) = (p+1)*(p+3). - Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2006
Also the area of twin prime rectangles. A twin prime rectangle is a rectangle whose sides are components of twin prime pairs. E.g. The twin prime pair (3,5) produces a 3x5 unit rectangle which has area 15 square units. - Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
A product of twin primes is of the form 36k^2-1 (cf. A136017, A002822). - Artur Jasinski (grafix(AT)csl.pl), Dec 12 2007
A072965(a(n)) = 1; A072965(m) mod A037074(n) > 0 for all m. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 29 2008
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REFERENCES
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Albert A. Mullin, "Bicomposites, twin primes, and arithmetic progression", Abstract 04T-11-48, Abstracts of AMS, Vol. 25, No. 4, 2004, p. 795.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
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FORMULA
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a(n) = A001359(n)* A006512(n). A000010(a(n))*A000203(a(n)) = (a(n)-3)*(a(n)+1). - Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 21 2006
a(n)=(A014574(n))^2 - 1. a(n+1)=(6*A002822(n))^2 - 1. - Lekraj Beedassy (blekraj(AT)yahoo.com), Sep 02 2006
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EXAMPLE
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a(2)=35 because 5*7=35, that is (5,7) is the 2nd pair of twin primes.
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MAPLE
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ZL:=[]:for p from 1 to 863 do if (isprime(p) and isprime(p+2) ) then ZL:=[op(ZL), (p*(p+2))]; fi; od; print(ZL); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 07 2007
for i from 1 to 150 do if ithprime(i+1) = ithprime(i) + 2 then print({ithprime(i)*ithprime(i+1)}); fi; od; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 19 2007
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MATHEMATICA
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s = Select[ Prime@ Range@170, PrimeQ[ # + 2] &]; s(s + 2) (from Robert G. Wilson v (rgwv(at)rgwv.com), Feb 21 2006)
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PROGRAM
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(PARI) g(n) = for(x=1, n, if(prime(x+1)-prime(x)==2, print1(prime(x)*prime(x+1)", "))) - Cino Hilliard (hillcino368(AT)gmail.com), Jul 28 2006
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CROSSREFS
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Cf. A000010, A000203, A001359, A006512, A014574.
Cf. A136017.
Adjacent sequences: A037071 A037072 A037073 this_sequence A037075 A037076 A037077
Sequence in context: A070161 A142591 A074480 this_sequence A107423 A027442 A074891
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KEYWORD
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nice,nonn
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AUTHOR
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Felice Russo (felice.russo(AT)katamail.com)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu)
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