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A068525
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Smallest k-almost prime between twin primes (for k >= 2).
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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,1
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COMMENTS
| 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
| Donovan Johnson, Table of n, a(n) for n=2..431
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Twin Primes
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EXAMPLE
| 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
| 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 [From Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 02 2010]
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PROG
| (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
| Cf. A001358 (semiprimes, with links to other almost primes), A001359 (lesser of twin primes).
Sequence in context: A065125 A177265 A192331 * A067755 A051858 A084709
Adjacent sequences: A068522 A068523 A068524 * A068526 A068527 A068528
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KEYWORD
| nonn
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AUTHOR
| Rick L. Shepherd (rshepherd2(AT)hotmail.com), Mar 21 2002
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EXTENSIONS
| a(27) - a(29) from Robert G. Wilson v (rgwv(AT)rgwv.com), Aug 02 2010
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