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A131016 Smallest semiprime == 1 (mod n). 1
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 (list; graph; refs; listen; history; text; internal format)
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 A291645

Adjacent sequences:  A131013 A131014 A131015 * A131017 A131018 A131019

KEYWORD

nonn

AUTHOR

Jonathan Vos Post, Sep 22 2007

STATUS

approved

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Last modified September 28 21:22 EDT 2021. Contains 347717 sequences. (Running on oeis4.)