A131016 Smallest semiprime == 1 (mod n).

4, 9, 4, 9, 6, 25, 15, 9, 10, 21, 34, 25, 14, 15, 46, 33, 35, 55, 39, 21, 22, 111, 93, 25, 26, 183, 55, 57, 146, 91, 94, 33, 34, 35, 106, 145, 38, 39, 118, 121, 206, 85, 87, 133, 46, 93, 95, 49, 295, 51, 205, 209, 213, 55, 111, 57, 58, 291, 119, 121, 62, 187, 253, 65, 326

Offset

1,1

Comments

This is to semiprimes A001358 as A034694 is to primes A000040. Conjecture: every semiprime occurs in this sequence. a(21)-a(65) from Robert G. Wilson v, Sep 21 2007

It is easy to prove that the first N>1 terms contain every semiprime < N. Assume the opposite: there is some semiprime pq that does not appear in the first pq-1 terms. This implies that n does not divide pq-1 for any n<pq. However, this is false because we can take n=pq-1. We see this behavior in the sequence quite often: a(5)=6, a(9)=10, a(13)=14, etc. - T. D. Noe, Sep 26 2007

Links

Robert G. Wilson v and T. D. Noe, Table of n, a(n) for n=1..1000

Formula

a(n) = MIN{k in A001358 and n|(k-1)}.

Mathematica

semiPrimeQ[x_] := Plus @@ Last /@ FactorInteger@ x == 2; sp = Select[ Range@ 346, semiPrimeQ@ # &]; f[1] = sp[[1]]; f[n_] := Block[{k = 1}, While[ Mod[ sp[[k]], n] != 1, k++ ]; sp[[k]] ]; Array[f, 65] (* Robert G. Wilson v *)

Crossrefs

Cf. A001358, A034694.

Cf. A085710.

Sequence in context: A204919 A113484 A061767 * A204996 A061369 A361400

Adjacent sequences: A131013 A131014 A131015 * A131017 A131018 A131019

Keyword

nonn

Author

Jonathan Vos Post, Sep 22 2007

Status

approved