Smarandache semiprimes

sean · 2010-04-01, 03:33

Sequence A046461 Sloane's OEIS, about finding semiprime Smarandache numbers (concatenation the positive integers, Sm(11)=1234567891011, etc.). The known values this sequence are 3, 4, 7, 34, 97. For example, Sm(34) = 2 * 6172839455055606570758085909601061116212631364146515661667.

Further searching indicates the only other possible members below 2300, are:

Code:

Sm(631)
Sm(691)
Sm(859)
Sm(1033)
Sm(1051)
Sm(1291)
Sm(1651)
Sm(1657)
Sm(1831)
Sm(1951)
Sm(2041)
Sm(2047)
Sm(2107)

Finding a factor any these numbers sufficient (after determing cofactor primality etc.) determine they are the sequence.

I've run 100 ecm curves with b1=10000 each candidate, but nothing with higher limits.

sean · 2010-04-01, 03:36

Hmm, for some reason the forum i.s losing two letter words like i.s from m.y posts.

EdH · 2010-04-01, 13:59

Quote:

Originally Posted by sean

Hmm, for some reason the forum i.s losing two letter words like i.s from m.y posts.

I suspect (and hope) this (and other anomalies) will only annoy today...

CRGreathouse · 2010-04-01, 14:21

Ugh, ,base,-sequences. I'll take Sm(631) t.o 250,000.

kar_bon · 2010-04-01, 15:15

Some weeks ago i begun to make a summary-page for Smarandache-type sequences but not yet time to complete everything and the FactorDB-issue for small numbers is annoying,too.

See here for Smarandache- and Reverse-Smarandache-sequences.

Jens K Andersen · 2010-04-01, 16:59

PrimeForm/GW has found Sm(5053) = 133283 * prp19099.

I'm not attempting to prove the prp.

CRGreathouse · 2010-04-01, 17:50

Quote:

Originally Posted by CRGreathouse

Ugh, ,base,-sequences. I'll take Sm(631) t.o 250,000.

If nothing goes wrong, I'll have it done through 35 digits (B1 = 1,000,000) tomorrow.

Jens K Andersen · 2010-04-02, 12:38

Sm(9706) = 2 * prp37716, found by PrimeForm/GW.

CRGreathouse · 2010-04-02, 12:39

Sm(631) = 414941628631826493984534937401473 * C1752

Working on Sm(691) now.

sean · 2010-04-05, 19:58

Many thanks for the Sm(631) and the results for higher n. In a few days I will submit some extra comments on the OEIS entry.

CRGreathouse · 2010-04-05, 21:47

Quote:

Originally Posted by sean

Many thanks for the Sm(631) and the results for higher n. In a few days I will submit some extra comments on the OEIS entry.

It would be really nice to find the next term, but that's going to take more than "a few days" unless you get a lot more people.

2010-04-01, 03:33	#1
sean Aug 2004 New Zealand 223 Posts	Smarandache semiprimes Sequence A046461 Sloane's OEIS, about finding semiprime Smarandache numbers (concatenation the positive integers, Sm(11)=1234567891011, etc.). The known values this sequence are 3, 4, 7, 34, 97. For example, Sm(34) = 2 * 6172839455055606570758085909601061116212631364146515661667. Further searching indicates the only other possible members below 2300, are: Code: Sm(631) Sm(691) Sm(859) Sm(1033) Sm(1051) Sm(1291) Sm(1651) Sm(1657) Sm(1831) Sm(1951) Sm(2041) Sm(2047) Sm(2107) Finding a factor any these numbers sufficient (after determing cofactor primality etc.) determine they are the sequence. I've run 100 ecm curves with b1=10000 each candidate, but nothing with higher limits.

2010-04-02, 12:39	#9
CRGreathouse Aug 2006 3·1,993 Posts	Sm(631) = 414941628631826493984534937401473 * C1752 Working on Sm(691) now. Last fiddled with by CRGreathouse on 2010-04-02 at 13:15

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2010-04-01, 03:36	#2
sean Aug 2004 New Zealand DF₁₆ Posts	Hmm, for some reason the forum i.s losing two letter words like i.s from m.y posts.

2010-04-01, 14:21	#4
CRGreathouse Aug 2006 3·1,993 Posts	Ugh, ,base,-sequences. I'll take Sm(631) t.o 250,000.

2010-04-01, 15:15	#5
kar_bon Mar 2006 Germany 2²·727 Posts	Some weeks ago i begun to make a summary-page for Smarandache-type sequences but not yet time to complete everything and the FactorDB-issue for small numbers is annoying,too. See here for Smarandache- and Reverse-Smarandache-sequences.

2010-04-01, 16:59	#6
Jens K Andersen Feb 2006 Denmark 2×5×23 Posts	PrimeForm/GW has found Sm(5053) = 133283 * prp19099. I'm not attempting to prove the prp.

2010-04-02, 12:38	#8
Jens K Andersen Feb 2006 Denmark 2·5·23 Posts	Sm(9706) = 2 * prp37716, found by PrimeForm/GW.

2010-04-05, 19:58	#10
sean Aug 2004 New Zealand 223 Posts	Many thanks for the Sm(631) and the results for higher n. In a few days I will submit some extra comments on the OEIS entry.