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A162491 Least prime dividing 2^n+3. 1
2, 5, 7, 11, 19, 5, 67, 131, 7, 5, 13, 7, 4099, 5, 7, 32771, 65539, 5, 262147, 29, 7, 5, 13, 7, 1549, 5, 7, 4057, 268435459, 5, 1073741827, 83, 7, 5, 13, 7, 61, 5, 7, 63727, 19, 5, 307, 11, 7, 5, 13, 7, 853, 5, 7, 967, 373, 5, 1422061, 36028797018963971, 7, 5, 13 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
All terms except for a(0)=2 are odd primes >= 5. (3 cannot divide 2^k+3 because 2 = -1 (mod 3).)
LINKS
FORMULA
If n=1 (mod 4), then a(n)=5 (since 2^4=1 (mod 5)).
If n=2 (mod 6) (or if n=1 (mod 3) but not (mod 4)), then a(n)=7 (since 2^3=1 (mod 7)).
EXAMPLE
a(0)=2 is the smallest prime factor of 2^0+3 = 4.
a(1)=5 is the smallest prime factor of 2^1+3 = 5.
PROG
(PARI) A162491(n)=factor(2^n+3)[1, 1]
/* more efficient for large numbers with small divisors: */
A162491(n)={my(p); while(Mod(2, p=nextprime(p+1))^n+3, ); p}
CROSSREFS
Sequence in context: A364649 A163695 A134641 * A152216 A045350 A179273
KEYWORD
nonn
AUTHOR
M. F. Hasler, Sep 09 2009
STATUS
approved

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Last modified April 21 23:44 EDT 2024. Contains 371886 sequences. (Running on oeis4.)