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A068525
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Smallest k-almost prime between twin primes (for k >= 2).
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5
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4, 12, 60, 72, 240, 192, 2112, 1152, 14592, 26112, 15360, 139968, 138240, 675840, 2101248, 737280, 4866048, 786432, 22118400, 36175872, 194641920, 63700992, 138412032, 169869312, 1321205760, 11123294208, 16357785600, 25669140480
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OFFSET
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2,1
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COMMENTS
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Because it is unknown whether an infinite number of twin primes exist, it is unknown whether this sequence is infinite.
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LINKS
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Donovan Johnson, Table of n, a(n) for n = 2..431
Eric Weisstein's World of Mathematics, Almost Prime
Eric Weisstein's World of Mathematics, Twin Primes
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EXAMPLE
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a(6)=240 because 240=2^4*3*5 is a 6-almost prime, 239 and 241 are twin primes and there is no 6-almost prime smaller than 240 which is between a pair of twin primes.
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MATHEMATICA
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f[n_] := Plus @@ Last /@ FactorInteger@n; p = 3; t = Table[0, {30}]; While[p < 26*10^9, If[ PrimeQ[p + 2], a = f[p + 1]; If[ t[[a]] == 0, t[[a]] = p + 1; Print[{a, p + 1}]]]; p = NextPrime@p]; t (* Robert G. Wilson v, Aug 02 2010 *)
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PROG
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(PARI) v=vector(32) for(n=3, 2250000000, if(n%1000000==0, print(n)); if(isprime(n) && isprime(n+2), k=bigomega(n+1); if(v[k]==0, v[k]=n+1; print(v[k], ", ", k)))); v
\\ The PARI program prints a progress mark per million integers examined. v[k] is loaded with the first k-almost prime encountered between primes and is printed upon discovery. The entire vector is printed at program completion (or can be printed after interrupting the PARI program with CTRL-C).
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CROSSREFS
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Cf. A001358 (semiprimes, with links to other almost primes), A001359 (lesser of twin primes), A014574, A075590.
Sequence in context: A177265 A243923 A192331 * A067755 A051858 A084709
Adjacent sequences: A068522 A068523 A068524 * A068526 A068527 A068528
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KEYWORD
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nonn
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AUTHOR
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Rick L. Shepherd, Mar 21 2002
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EXTENSIONS
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a(27) - a(29) from Robert G. Wilson v, Aug 02 2010
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STATUS
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approved
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