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A317556 a(n) is the smallest composite k such that k divides 2^(k*n-1) - 1. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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, ...

LINKS

Table of n, a(n) for n=1..54.

EXAMPLE

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

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 *)

PROG

(PARI) isok(k, n)=Mod(2, k)^(k*n-1)==1;

a(n)={my(k=2); while (isprime(k)||!isok(k, n), k++); k; }

CROSSREFS

Cf. A001567, A102457.

Sequence in context: A300327 A289305 A309285 * A006107 A015371 A328665

Adjacent sequences:  A317553 A317554 A317555 * A317557 A317558 A317559

KEYWORD

nonn

AUTHOR

Altug Alkan, Sep 15 2018

STATUS

approved

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Last modified April 4 06:59 EDT 2020. Contains 333213 sequences. (Running on oeis4.)