A252669 a(n) is the smallest integer k such that n*k mod (n+k) = 1, or -1 if no such k exists.

1, 3, 2, 13, 8, 31, 3, 5, 32, 91, 50, 17, 4, 183, 98, 241, 12, 7, 162, 381, 5, 75, 30, 553, 288, 651, 46, 129, 392, 23, 6, 9, 76, 55, 578, 1261, 100, 47, 722, 1561, 17, 311, 7, 105, 968, 27, 18, 413, 1152, 11, 1250, 489, 228, 2863, 34, 3081, 8, 615, 1682, 217, 1800, 707

Offset: 1

Author

Alex Ratushnyak, Jan 02 2015

Keywords

• nonn

Crossrefs

Cf. A063427.

Programs

Mathematica

sik[n_]:=Module[{k=1},While[Mod[n*k,n+k]!=1,k++];k]; Array[sik,70] (* Harvey P. Dale, Aug 15 2015 *)

PARI

a(n) = k=1; while ((n*k) % (n+k) != 1, k++); k; \\ Michel Marcus, Jan 08 2015

Python

import math
for n in range(1,333):
    res=-1
    for k in range(2**31-1):
        if ((n*k) % (n+k) == 1):
            res=k
            break
    print(res, end=', ')

Formula

a(a(n)) <= n.