%I #12 Sep 08 2019 04:35:37

%S 2,4,6,10,16,16,70,136,210,210,442,786,786,786,6450,53110,53110,

%T 247690,303810,303810,813450,3443146,5889382,9327220,10068256,

%U 63916062,63916062,63916062,285847290,285847290,285847290,285847290,370793956,370793956,370793956,370793956

%N Smallest integer > 0 so that its remainders modulo the first n primes are less than half their respective moduli.

%H Bert Dobbelaere, <a href="/A327408/b327408.txt">Table of n, a(n) for n = 1..53</a>

%e a(6) = 16.

%e 16 mod 2 = 0 < 2/2

%e 16 mod 3 = 1 < 3/2

%e 16 mod 5 = 1 < 5/2

%e 16 mod 7 = 2 < 7/2

%e 16 mod 11 = 5 < 11/2

%e 16 mod 13 = 3 < 13/2

%e 16 is the smallest integer > 0 satisfying these inequalities for the first 6 primes.

%o (PARI) isok(k, vp) = {for (i=1, #vp, if ((k % vp[i]) >= vp[i]/2, return (0));); return (1);}

%o a(n) = {my(k=1, vp = primes(n)); while (!isok(k, vp), k++); k;} \\ _Michel Marcus_, Sep 08 2019

%Y Companion sequence of A327409.

%Y Cf. A002110, A306582, A306612.

%K nonn

%O 1,1

%A _Bert Dobbelaere_, Sep 07 2019