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A271801
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Smallest composite k such that k divides (n^(k-1)-1)/(n-1), n > 1.
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3
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341, 91, 85, 217, 217, 25, 9, 91, 91, 133, 65, 85, 15, 341, 91, 9, 25, 49, 21, 221, 169, 91, 25, 91, 9, 121, 145, 15, 49, 49, 25, 85, 35, 9, 403, 133, 39, 341, 121, 21, 529, 25, 9, 133, 133, 65, 49, 25, 51, 91, 265, 9, 55, 91, 57, 25, 341, 15, 341, 91, 9, 481, 65, 33, 469, 49, 25, 35, 169, 9, 85, 65
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OFFSET
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2,1
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COMMENTS
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Smallest pseudoprime k to base n such that gcd(k,n-1)=1.
Theorem (R. Steuerwald, 1948): if k is a pseudoprime to base b and gcd(k,b-1)=1, then (b^k-1)/(b-1) is a pseudoprime to base b.
From Robert Israel, Apr 14 2016: (Start)
a(n) is odd.
If m == n (mod a(n)) then a(m) <= a(n).
a(n) = 9 iff n == -1 (mod 9).
a(n) = 15 iff n == -1 (mod 15) but not (mod 9).
The first case where a(n) is not a semiprime (A001358) is a(383) = 561. (End)
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LINKS
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Robert Israel, Table of n, a(n) for n = 2..10000
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MAPLE
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Comps:= remove(isprime, [seq(k, k=9..10^6, 2)]):
f:= proc(n) local k;
for k in Comps do
if (n^(k-1)-1)/(n-1) mod k = 0 then return k fi
od:
error "ran out of composites"
end proc:
seq(f(n), n=2..100); # Robert Israel, Apr 14 2016
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MATHEMATICA
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Table[SelectFirst[Range[10^3], CompositeQ@ # && Divisible[(n^(# - 1) - 1)/(n - 1), #] &], {n, 2, 73}] (* Michael De Vlieger, Apr 14 2016, Version 10 *)
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PROG
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(PARI) a(n) = {my(k = 4); while ((n^(k-1)-1)/(n-1) % k, k++; if (isprime(k), k++)); k; } \\ Michel Marcus, Apr 14 2016
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CROSSREFS
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Cf. A001358.
Sequence in context: A222927 A298908 A057598 * A322120 A250199 A271874
Adjacent sequences: A271798 A271799 A271800 * A271802 A271803 A271804
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KEYWORD
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nonn
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AUTHOR
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Thomas Ordowski, Apr 14 2016
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EXTENSIONS
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More terms from Michael De Vlieger, Apr 14 2016
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STATUS
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approved
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