

A068525


Smallest kalmost 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
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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 6almost prime, 239 and 241 are twin primes and there is no 6almost 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 kalmost 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 CTRLC).


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



