A192419 -id:A192419 - cp's OEIS frontend

A016726 Smallest k such that 1, 4, 9, ..., n^2 are distinct mod k.

1, 2, 6, 9, 10, 13, 14, 17, 19, 22, 22, 26, 26, 29, 31, 34, 34, 37, 38, 41, 43, 46, 46, 53, 53, 53, 58, 58, 58, 61, 62, 67, 67, 71, 71, 73, 74, 79, 79, 82, 82, 86, 86, 89, 94, 94, 94, 97, 101, 101, 103, 106, 106, 109, 113, 113, 118, 118, 118, 122, 122, 127, 127, 131, 131, 134

Offset: 1

bernie(AT)wagnerpa.com (Bernie McCabe)

This is the sequence of discriminators of the squares A000290, in the terminology of Arnold et al. - M. F. Hasler, May 04 2016

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.

Cf. A001751, A192419 (cubes), A192420 (4th powers), A347693.

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

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 *)

A016726_vec(nMax)={my(S=[], a=1); vector(nMax, n, S=concat(S, n^2); while(#Set(S%a)M. F. Hasler, May 04 2016

A016726(n)=if(n>4,min(nextprime(2*n),2*nextprime(n)),[1,2,6,9][n]) \\ M. F. Hasler, May 04 2016

For n > 4, a(n) is smallest k >= 2n such that k = p or k = 2p, p a prime.

A192420 Smallest k such that 1^4, 2^4, 3^4,... ,n^4 are distinct modulo k.

Original entry on oeis.org

1, 2, 6, 9, 11, 14, 14, 18, 19, 22, 22, 31, 31, 31, 31, 38, 38, 38, 38, 43, 43, 46, 46, 59, 59, 59, 59, 59, 59, 62, 62, 67, 67, 71, 71, 79, 79, 79, 79, 83, 83, 86, 86, 94, 94, 94, 94, 103, 103, 103, 103, 107, 107, 118, 118, 118, 118, 118, 118, 127, 127, 127, 127, 131, 131, 134, 134, 139, 139

Offset: 1

R. J. Mathar, Jun 30 2011

nonn

The discriminator D(4,n).

Alois P. Heinz, Table of n, a(n) for n = 1..1000
P. Moree, H. Roskam, On an arithmetical function related to Euler's totient and the discriminator, Fib. Quart. 33 (4) (1995), 332-340

Cf. A016726, A192419.

dis := proc(j,n) local k,s,i; for k from 1 do s := {} ; for i from 1 to n do s := s union { (i^j) mod k} ; end do: if nops(s) = n then return k; end if; end do: end proc:
A192420 := proc(n) dis(4,n) ; end proc:

a[n_] := For[k = 1, True, k++, If[Unequal @@ PowerMod[Range[n], 4, k], Return[k]]]; Array[a, 100] (* Jean-François Alcover, May 18 2018 *)

A192420(nMax,f=n->n^4)={my(S=[],a=1); vector(nMax,n,S=concat(S,f(n));while(#Set(S%a)M. F. Hasler, May 04 2016

A272633 Discriminator of the primes: Least m > 0 such that (prime(1),...,prime(n)) are all different mod m; a(0) = 0 by convention.

Original entry on oeis.org

0, 1, 2, 4, 6, 7, 7, 13, 13, 13, 19, 19, 19, 23, 23, 23, 31, 31, 31, 33, 37, 37, 43, 43, 47, 49, 53, 53, 53, 55, 61, 63, 67, 73, 73, 75, 75, 79, 83, 83, 89, 89, 91, 91, 97, 103, 103, 109, 113, 113, 115, 117, 119, 121, 121, 121, 121, 121, 139, 139, 141, 141, 151, 153, 157, 157, 159, 167, 169, 169, 175, 181, 181, 183, 187

Offset: 0

M. F. Hasler, May 04 2016

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..10000 (first 5001 terms from M. F. Hasler)
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.

Cf. A016726, A192419, A192420.

a:= proc(n) option remember; local m;
      for m from `if`(n=1, 1, a(n-1)) while
        n<>nops({seq(ithprime(i) mod m, i=1..n)})
      do od; m
    end: a(0):=0:
seq(a(n), n=0..80);  # Alois P. Heinz, May 04 2016

a[0]=0; a[n_]:=Block[{m=1}, While[Length@ DeleteDuplicates@ Mod[Prime@ Range@ n, m] != n, m++]; m]; a /@ Range[0, 74] (* Giovanni Resta, May 04 2016 *)

A272633(nMax)={my(S=[],a=1);vector(nMax, n, S=concat(S,prime(n)); while(#Set(S%a)

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A016726 Smallest k such that 1, 4, 9, ..., n^2 are distinct mod k.

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A192420 Smallest k such that 1^4, 2^4, 3^4,... ,n^4 are distinct modulo k.

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A272633 Discriminator of the primes: Least m > 0 such that (prime(1),...,prime(n)) are all different mod m; a(0) = 0 by convention.

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