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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

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

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

Adjacent sequences:  A068522 A068523 A068524 * A068526 A068527 A068528

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 April 17 19:51 EDT 2021. Contains 343070 sequences. (Running on oeis4.)