A317556 a(n) is the smallest composite k such that k divides 2^(k*n-1) - 1.

341, 80519, 15, 511, 65, 42671, 15, 161, 445, 35551, 15, 2047, 85, 80129, 15, 1561, 33, 190679, 15, 983927, 85, 511, 15, 11303, 345, 2201, 15, 217, 65, 188393, 15, 39071, 129, 2047, 15, 8727391, 33, 63457, 15, 511, 65, 2417783, 15, 64759, 85, 2921, 15, 1898777, 133, 119063, 15, 2263, 65, 10097

Offset: 1

Author

Altug Alkan, Sep 15 2018

Keywords

• nonn

Comments

Inspired by A001567.

Based on definition of a(n), certain terms are easy to determine, i.e., a(4*t+3) = 15 and a(20*t+17) = 33 for all t >= 0.

Least k > 1 such that k divides 2^(k*n-1) - 1 (for n >= 1) are 3, 80519, 3, 7, 3, 31, 3, 127, 3, 7, 3, 23, 3, 8191, 3, 7, 3, 131071, 3, 524287, 3, 7, 3, 47, ...

Examples

			a(1) = A001567(1) = 341.
		

Crossrefs

Cf. A001567, A102457.

Programs

Mathematica

a[n_] := Block[{k = 9}, While[PrimeQ[k] || PowerMod[2, k*n - 1, k] != 1, k += 2]; k]; Array[a, 54] (* Giovanni Resta, Sep 16 2018 *)

PARI

isok(k,n)=Mod(2, k)^(k*n-1)==1;
a(n)={my(k=2); while (isprime(k)||!isok(k,n), k++); k; }