A162491 Least prime dividing 2^n+3.

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

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

Chai Wah Wu, Table of n, a(n) for n = 0..699

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

Adjacent sequences: A162488 A162489 A162490 * A162492 A162493 A162494

Keyword

nonn

Author

M. F. Hasler, Sep 09 2009

Status

approved