

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

Robert Israel, Table of n, a(n) for n = 1..10000


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:
Res; # Robert Israel, Sep 12 2018


MATHEMATICA

terms = 100;
A045309 = Select[Prime[Range[2 terms]], Mod[#, 3] != 1&];
a[n_] := PowerMod[2, 1/3, A045309[[n]]];
Array[a, terms] (* JeanFrançois Alcover, Feb 27 2019 *)


CROSSREFS

Cf. A040028, A045309, A059940, A060914, A060122, A060123, A060124.
Sequence in context: A076550 A062269 A244508 * A002964 A166966 A247843
Adjacent sequences: A060118 A060119 A060120 * A060122 A060123 A060124


KEYWORD

nonn


AUTHOR

Klaus Brockhaus, Mar 02 2001


STATUS

approved



