A327408 Smallest integer > 0 so that its remainders modulo the first n primes are less than half their respective moduli.
2, 4, 6, 10, 16, 16, 70, 136, 210, 210, 442, 786, 786, 786, 6450, 53110, 53110, 247690, 303810, 303810, 813450, 3443146, 5889382, 9327220, 10068256, 63916062, 63916062, 63916062, 285847290, 285847290, 285847290, 285847290, 370793956, 370793956, 370793956, 370793956
Offset: 1
Keywords
Examples
a(6) = 16. 16 mod 2 = 0 < 2/2 16 mod 3 = 1 < 3/2 16 mod 5 = 1 < 5/2 16 mod 7 = 2 < 7/2 16 mod 11 = 5 < 11/2 16 mod 13 = 3 < 13/2 16 is the smallest integer > 0 satisfying these inequalities for the first 6 primes.
Links
- Bert Dobbelaere, Table of n, a(n) for n = 1..53
Programs
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PARI
isok(k, vp) = {for (i=1, #vp, if ((k % vp[i]) >= vp[i]/2, return (0));); return (1);} a(n) = {my(k=1, vp = primes(n)); while (!isok(k, vp), k++); k;} \\ Michel Marcus, Sep 08 2019