

A060121


First solution mod p of x^3 = 2 for primes p such that only one solution exists.


6



0, 2, 3, 7, 8, 16, 26, 5, 21, 18, 38, 49, 50, 16, 26, 6, 81, 54, 98, 70, 157, 161, 58, 147, 21, 86, 92, 197, 50, 249, 137, 184, 119, 45, 45, 261, 198, 61, 176, 143, 51, 103, 221, 72, 11, 219, 35, 86, 385, 384, 141, 143, 225, 92, 245, 533, 557, 473, 170, 375, 516
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OFFSET

1,2


COMMENTS

Solutions mod p are represented by integers from 0 to p1. For i > 1, i is a solution mod p of x^3 = 2 iff p is a prime factor of i^32 and p > i (cf. comment to A059940). i^32 has at most two prime factors > i. Hence i is a solution mod p of x^3 = 2 for at most two different p and therefore no integer occurs more than twice in this sequence. There are integers which do occur twice, e.g. 16, 21, 26 (cf. A060914). Moreover, no integer occurs more than twice in A060121, A060122, A060123 and A060124 taken together.


LINKS



FORMULA

a(n) = first (only) solution mod p of x^3 = 2, where p is the nth prime such that x^3 = 2 has only one solution mod p, i.e. p is the nth term of A045309.


EXAMPLE

a(9) = 21, since 47 is the ninth term of A045309 and 21 is the only solution mod 47 of x^3 = 2.


MAPLE

Res:=0, 2: count:= 2: p:= 3:
while count < 100 do
p:= nextprime(p);
if p mod 3 = 2 then
count:= count+1;
Res:= Res, numtheory:mroot(2, 3, p);
fi
od:


MATHEMATICA

terms = 100;
A045309 = Select[Prime[Range[2 terms]], Mod[#, 3] != 1&];
a[n_] := PowerMod[2, 1/3, A045309[[n]]];


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



