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A059940 Smallest prime p such that x = n is a solution mod p of x^3 = 2, or 0 if no such prime exists. 6
3, 5, 31, 41, 107, 11, 17, 727, 499, 443, 863, 439, 457, 3373, 23, 1637, 53, 6857, 31, 47, 5323, 811, 6911, 919, 29, 19681, 439, 739, 13499, 29789, 43, 7187, 43, 461, 23327, 50651, 59, 2579, 2909, 22973, 2179, 15901, 14197, 293, 1187, 34607, 11059 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Solutions mod p are represented by integers from 0 to p-1. The following equivalences hold for n > 1: There is a prime p such that n is a solution mod p of x^3 = 2 iff n^3-2 has a prime factor > n; n is a solution mod p of x^3 = 2 iff p is a prime factor of n^3-2 and p > n.

n^3-2 has at most two prime factors > n, consequently these factors are the only primes p such that n is a solution mod p of x^3 = 2. For n such that n^3-2 has no prime factor > n (the zeros in the sequence; they occur beyond the last entry shown in the database) see A060591. For n such that n^3-2 has two prime factors > n, cf. A060914.

LINKS

Table of n, a(n) for n=2..48.

FORMULA

If n^3-2 has prime factors > n, then a(n) = least of these prime factors, else a(n) = 0.

EXAMPLE

a(2) = 3, since 2 is a solution mod 3 of x^3 = 2 and 2 is not a solution mod p of x^3 = 2 for prime p = 2. Although 2^3 = 2 mod 2, prime 2 is excluded because 0 < 2 and 2 = 0 mod 2. a(5) = 41, since 5 is a solution mod 41 of x^3 = 2 and 5 is not a solution mod p of x^3 = 2 for primes p < 41. Although 5^3 = 2 mod 3, prime 3 is excluded because 3 < 5 and 5 = 2 mod 3.

CROSSREFS

Cf. A040028, A060121, A060122, A060123, A060124, A060591, A060914.

Sequence in context: A189739 A035410 A290487 * A106893 A175097 A217320

Adjacent sequences:  A059937 A059938 A059939 * A059941 A059942 A059943

KEYWORD

nonn

AUTHOR

Klaus Brockhaus, Mar 02 2001

STATUS

approved

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Last modified October 21 01:35 EDT 2021. Contains 348131 sequences. (Running on oeis4.)