

A317556


a(n) is the smallest composite k such that k divides 2^(k*n1)  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
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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*n1)  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*n1)==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



