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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 October 3 19:04 EDT 2023. Contains 365870 sequences. (Running on oeis4.)