A218121 -id:A218121

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A218123

Denominators of terms of the sequence {c(n)} defined in A218121.

+20
2

1, 2, 2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7, 7, 7, 7, 7, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 31, 31, 31, 31, 31, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 43, 43, 43, 43, 43, 47, 47

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

It is easy to see that every prime is in the sequence.

LINKS

Table of n, a(n) for n=1..80.

MAPLE

ispfree := proc(a, b)

local alow ;

alow := floor(a);

if nextprime(alow) < b then

false;

else

true;

end if;

end proc:

A218121c := proc(n)

option remember;

local k ;

if n = 1 then

return 1;

elif n = 2 then

return 5/2 ;

else

if ispfree(ithprime(n)/procname(n-1), ithprime(n+1)/procname(n-1)) then

return procname(n-1) ;

end if ;

for k from n by -1 do

if ispfree( ithprime(n)*ithprime(k)/ithprime(n+1), ithprime(k) )

and ithprime(n+1)/ithprime(k) > procname(n-1) then

return ithprime(n+1)/ithprime(k) ;

end if;

end do:

end if;

end proc:

A218123 := proc(n)

denom(A218121c(n)) ;

end proc: # R. J. Mathar, Dec 02 2012

CROSSREFS

Cf. A218121, A217871, A217689, A217691, A217833, A217884.

KEYWORD

nonn,frac

AUTHOR

Vladimir Shevelev, Oct 21 2012

STATUS

approved

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