OFFSET
1,2
COMMENTS
This is the sequence of discriminators of the squares A000290, in the terminology of Arnold et al. - M. F. Hasler, May 04 2016
LINKS
T. D. Noe, Table of n, a(n) for n=1..1000
Arnold, L. K.; Benkoski, S. J.; and McCabe, B. J.; The discriminator (a simple application of Bertrand's postulate). Amer. Math. Monthly 92 (1985), 275-277.
FORMULA
For n > 4, a(n) is smallest k >= 2n such that k = p or k = 2p, p a prime.
MATHEMATICA
a[n_] := (k = 2n; While[ Not[PrimeQ[k] || PrimeQ[k/2]], k++]; k); a[1]=1; a[2]=2; a[3]=6; a[4]=9; Table[a[n], {n, 1, 66}] (* Jean-François Alcover, Nov 30 2011, after formula *)
sk[n_]:=Module[{k=2n, n2=Range[n]^2}, While[Max[Tally[Mod[n2, k]][[All, 2]]]> 1, k++]; k]; Join[{1, 2}, Array[sk, 70, 3]] (* Harvey P. Dale, Oct 16 2016 *)
PROG
(Haskell)
a016726 n = a016726_list !! (n-1)
a016726_list = [1, 2, 6, 9] ++ (f 5 $ drop 4 a001751_list) where
f n qs'@(q:qs) | q < 2*n = f n qs
| otherwise = q : f (n+1) qs'
-- Reinhard Zumkeller, Jun 20 2011
(PARI) A016726_vec(nMax)={my(S=[], a=1); vector(nMax, n, S=concat(S, n^2); while(#Set(S%a)<n, a++); a)} \\ M. F. Hasler, May 04 2016
(PARI) A016726(n)=if(n>4, min(nextprime(2*n), 2*nextprime(n)), [1, 2, 6, 9][n]) \\ M. F. Hasler, May 04 2016
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
bernie(AT)wagnerpa.com (Bernie McCabe)
STATUS
approved