A250209 a(n) = least k such that k * n is in A072226, or 0 if no such k exists.

2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 5, 1, 2, 2, 1, 2, 1, 6, 1, 1, 2, 5, 1, 1, 1, 1, 1, 8, 34, 8, 1, 2, 1, 10, 1, 2, 350, 2, 1, 111, 4, 1, 3, 16, 4, 15, 28, 3, 1, 206, 3, 10, 2, 1, 1, 2, 3, 1, 15, 637, 12, 1, 4, 22, 17, 104, 4, 2, 1012, 1, 1

Offset: 1

Author

Eric Chen, Jan 18 2015

Keywords

• nonn

Comments

Conjecture: a(n) > 0 for all n.

a(n) is currently unknown for n = 121, 124, 143, 162, 171, 172, 185, 188, 197, 215, ..., for which we have n * a(n) > 130000.

a(121) = (A117545(2048))/11 and they are both currently unknown.

A117545(2^n) = a(A064549(n)).

a(130) = 917, a(144) = 820, a(164) = 720, a(201) = 606. - Max Alekseyev, Dec 04 2024

Links

• Eric Chen, Table of n, a(n) for n = 1..120
• Eric Chen, Table of n, a(n) for n = 1..300 status

Programs

Mathematica

Table[k=1; While[!PrimeQ[Cyclotomic[n*k, 2]], k++]; k, {n, 43}]

PARI

a(n) = {k = 1; while (!isprime(polcyclo(k*n, 2)), k++); k;} \\ Michel Marcus, Jan 18 2015