0,1

Let f(m)= A051699(m) = exact distance from m to its closest prime (including m itself). Then a(n) = min { m : f(m) = 3n}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007

a(n) = min {m : A051699(m) = 3n}. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007

a(3)=532 where 532+3*3 is prime and all numbers below 532 have a distance smaller or larger than 3n=9 to their nearest primes, and there is no prime within a distance of 8 to 532.

A051699 := proc(m) if isprime(m) then 0 ; elif m <= 2 then op(m+1, [2, 1]) ; else min(nextprime(m)-m, m-prevprime(m)) ; fi ; end: A132470 := proc(n) local m ; if n = 0 then RETURN(2); else for m from 0 do if A051699(m) = 3 * n then RETURN(m) ; fi ; od: fi ; end: seq(A132470(n), n=0..18) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007

Cf. A051728.

Sequence in context: A067204 A120551 A120547 this_sequence A067851 A072415 A121768

Adjacent sequences: A132467 A132468 A132469 this_sequence A132471 A132472 A132473

nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Sep 03 2007

Corrected by Dean Hickerson, Sep 05 2007

Both this sequence and A051728 should be checked. There are two possibilities for confusion in each case. In defining f(m), does one allow or exclude m itself, in case m is a prime? In defining a(n), does one require (here) that f(m) = 3n or only that >= 3n, or (in A051728) that f(m) = 2n or only >= 2n? Probably there should be several sequences, to include all the possibilities in each case. - njas, Nov 18 2007. Added Nov 20, 2007: R. J. Mathar has now clarified the definition of the present sequence.

Corrected and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 18 2007