A327409 Smallest integer > 0 so that its remainders modulo the first n primes are at least half their respective moduli.

1, 5, 23, 53, 53, 293, 503, 713, 1439, 1439, 16673, 16673, 16673, 16673, 16673, 16673, 16673, 298583, 728153, 728153, 728153, 19420253, 19420253, 66663659, 207178199, 384974819, 384974819, 384974819, 546086693, 546086693, 8504041103, 22060162703, 60826761629, 60826761629

Offset: 1

Author

Bert Dobbelaere, Sep 07 2019

Keywords

• nonn

Examples

			a(6) = 293.
293 mod 2 = 1 >= 2/2
293 mod 3 = 2 >= 3/2
293 mod 5 = 3 >= 5/2
293 mod 7 = 6 >= 7/2
293 mod 11 = 7 >= 11/2
293 mod 13 = 7 >= 13/2
293 is the smallest integer > 0 satisfying these inequalities for the first 6 primes.
		

Links

• Bert Dobbelaere, Table of n, a(n) for n = 1..50

Crossrefs

Companion sequence of A327408.

Cf. A002110, A306582, A306612.

Programs

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