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A068525 Smallest k-almost prime between twin primes (for k >= 2). 5
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; text; internal format)
OFFSET
2,1
COMMENTS
Because it is unknown whether an infinite number of twin primes exist, it is unknown whether this sequence is infinite.
LINKS
Eric Weisstein's World of Mathematics, Almost Prime
Eric Weisstein's World of Mathematics, Twin Primes
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.
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 (* Robert G. Wilson v, Aug 02 2010 *)
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).
CROSSREFS
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
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Mar 21 2002
EXTENSIONS
a(27) - a(29) from Robert G. Wilson v, Aug 02 2010
STATUS
approved

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Last modified May 23 20:54 EDT 2024. Contains 372765 sequences. (Running on oeis4.)