

A284721


Smallest odd prime that is relatively prime to 2n+1.


3



3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 11, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 5, 3, 3, 7, 3, 3, 5
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OFFSET

0,1


COMMENTS

More than the usual number of terms are shown in order to distinguish this from A239278.
a(n) = smallest odd prime missing from rad(2*n+1).
If rad(2m+1) = rad(2n+1), a(m) = a(n) (cf. A007947).  Bob Selcoe, Apr 04 2017


LINKS

Table of n, a(n) for n=0..100.


FORMULA

a(n) = 3 unless n == 1 (mod 3).
For all n >= 2, a(n) < 3*log(2*n+1). Also, for all n >= 1, a(n) <5*log(2*n+1). [Upper bound corrected by N. J. A. Sloane, Apr 15 2017. Thanks to Bob Selcoe for pointing out that the old bound failed at n=1.]


PROG

(PARI) a(n) = my(p=3); while(gcd(2*n+1, p) != 1, p=nextprime(p+1)); p; \\ Michel Marcus, Apr 04 2017


CROSSREFS

Similar to but different from A239278.
Cf. A007947, A284722, A284723.
Sequence in context: A092553 A112755 A239278 * A126659 A246917 A102294
Adjacent sequences: A284718 A284719 A284720 * A284722 A284723 A284724


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, Apr 04 2017


STATUS

approved



