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

1,2

Links

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

Example

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.

Prog

(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

Crossrefs

Companion sequence of A327408.

Cf. A002110, A306582, A306612.

Sequence in context: A127200 A147113 A135771 * A140811 A247657 A241099

Adjacent sequences: A327406 A327407 A327408 * A327410 A327411 A327412

Keyword

nonn

Author

Bert Dobbelaere, Sep 07 2019

Status

approved