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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A269299 Maximum number of times a nine-digit number with non-repeating, nonzero digits can be divided by the n-th prime until a non-integer result is returned. 0
 16, 13, 7, 7, 5, 5, 5, 4, 4, 3, 3, 3, 3, 3, 3, 3, 2, 3, 3, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 1, 2, 2, 2, 2, 2, 2, 1, 3, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence was constructed with a simple game in mind, one done by hand or by calculator, where one takes a nine-digit number with non-repeating nonzero digits and divides it by three until a non-integer result is returned. The potential best play is then of interest for this game, or the maximum number of times three divides such a number. The sequence extends this idea to all primes under the same rules and outputs the maximum number of times the n-th prime divides a number in this form. The largest such prime that would give a nonzero solution is the 6289143rd prime, namely 109739359. LINKS Table of n, a(n) for n=1..96. EXAMPLE For n=2, 3 divides 618597324 13 times, and this is the highest achievable valuation. In comparison, if the rules regarding nonzero and non-repeating were lifted, the number 3^18 = 387420489 would be allowed, and a(2) would be 18. MAPLE with(LinearAlgebra)*with(combinat)*with(numtheory): A := permute(9): B := 0: for d to 6289143 do a[d] := 0: end do: for i to factorial(9) do B := ifactors(Determinant(Multiply(`<|>`(`<, >`(100000000), `<, >`(10000000), `<, >`(1000000), `<, >`(100000), `<, >`(10000), `<, >`(1000), `<, >`(100), `<, >`(10), `<, >`(1)), Transpose(convert(A[i], Matrix))))): C := nops([op(B[2])]): for j to C do if a[pi(B[2, j, 1])] < B[2, j, 2] then a[pi(B[2, j, 1])] := B[2, j, 2]: end if: end do: end do: seq(a[i], i = 1 .. 500); MATHEMATICA s = FromDigits /@ Permutations@ Range@ 9; Table[Max@ Map[Length@ NestWhileList[#/Prime@ n &, #, IntegerQ] &, s], {n, 40}] - 2 (* Michael De Vlieger, Feb 23 2016 *) PROG (PARI) a(n) = {my(p=prime(n)); my(mv = 0); for (i=0, 9!, mv = max(valuation(subst(Pol(numtoperm(9, i)), x, 10), p), mv); ); mv; } \\ Michel Marcus, Feb 26 2016 CROSSREFS Sequence in context: A291426 A299524 A070534 * A070577 A184752 A291468 Adjacent sequences: A269296 A269297 A269298 * A269300 A269301 A269302 KEYWORD nonn,base AUTHOR Aaron Benham, Feb 21 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 3 10:25 EDT 2023. Contains 363110 sequences. (Running on oeis4.)