

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



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



KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



