The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A266620 a(n) = least non-divisor of n!. 2
 2, 3, 4, 5, 7, 7, 11, 11, 11, 11, 13, 13, 17, 17, 17, 17, 19, 19, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 31, 31, 37, 37, 37, 37, 37, 37, 41, 41, 41, 41, 43, 43, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 59, 59, 59, 59, 61, 61, 67, 67, 67, 67, 67, 67, 71 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It appears that a(n) = A151800(n) with the exception of n = 3. - Robert Israel, Jan 13 2016 LINKS Robert Israel, Table of n, a(n) for n = 1..10000 FORMULA a(n) = min_{k >= 1} prime(k)^(1 + v(n!, prime(k))) where v(m, p) is the p-adic order of m. - Robert Israel, Jan 13 2016 a(n) = prime(pi(n) + 1) except for n = 3, in which case the least non-divisor of 3! is 4, not 5. - Alonso del Arte, Sep 23 2017 EXAMPLE For n = 4 the least non-divisor of 4! = 24 = 2^3 * 3 is 5. For n = 5 the least non-divisor of 5! = 120 = 2^3 * 3 * 5 is 7. MAPLE N:= 100: # to get a(1)..a(N) m:= 1 + numtheory:-pi(N): Primes:= [seq(ithprime(i), i=1..m)]: for i from 1 to m do pindex[Primes[i]]:= i od: V:= Vector(m): k:= 0: for n from 1 to N do for f in ifactors(n)[2] do q:= pindex[f[1]]; V[q]:= V[q] + f[2]; k:= max(k, q); od: a[n]:= min(seq(Primes[i]^(1+V[i]), i=1..k), Primes[k+1]); od: seq(a[n], n=1..N); # Robert Israel, Jan 13 2016 MATHEMATICA Table[Complement[Range[2n], Divisors[n!]][[1]], {n, 30}] (* Alonso del Arte, Sep 23 2017 *) Table[Block[{m = n!, k = n + 1}, While[Divisible[m, k], k++]; k], {n, 67}] (* Michael De Vlieger, Sep 23 2017 *) PROG (Python) from sympy import nextprime def A266620(n): return 4 if n == 3 else nextprime(n) # Chai Wah Wu, Feb 22 2023 CROSSREFS Cf. A007918, A007978, A066169, A115627, A151800. Sequence in context: A348531 A237824 A227972 * A222415 A022473 A214921 Adjacent sequences: A266617 A266618 A266619 * A266621 A266622 A266623 KEYWORD nonn,easy AUTHOR Jeffrey Shallit, Jan 01 2016 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 4 21:13 EDT 2023. Contains 363130 sequences. (Running on oeis4.)