OFFSET
1,1
COMMENTS
From Sean A. Irvine, Apr 15 2010, updated Oct 08 2015: (Start)
5053 and 9706 are definite terms of the sequence.
The next potential term is 1651.
A007908(1651) is composite, but has no known prime factor, and its least prime factor likely has at least 45 digits. (End)
If k is a multiple of 10, then k is not a term. - Chai Wah Wu, Jan 22 2020
From Jon E. Schoenfield, Oct 07 2023: (Start)
k cannot be a term if any of the following are true:
4|k and k > 4 (2*2 would divide the concatenation)
6|k or 6|k-2 (2*3 " " " " )
9|k or 9|k-8 (3*3 " " " " )
10|k (2*5 " " " " )
15|k or 15|k-5 (3*5 " " " " )
25|k (5*5 " " " " ) (End)
LINKS
Patrick De Geest, Normal Smarandache Concatenated Numbers, Prime factors from 1 up to n.
M. Fleuren, Factors and primes of Smarandache sequences.
M. Fleuren, Smarandache Factors and Reverse factors.
Carlos Rivera, Puzzle 8. Primes by Listing, The Prime Puzzles and Problems Connection.
EXAMPLE
MATHEMATICA
Select[Range[100], Length@FactorInteger@FromDigits@Flatten@IntegerDigits@Range@# == 2 &] (* Robert Price, Oct 11 2019 *)
Select[Range[100], PrimeOmega[FromDigits[Flatten[IntegerDigits/@Range[#]]]] == 2&] (* Harvey P. Dale, Sep 10 2022 *)
CROSSREFS
KEYWORD
nonn,hard,base,more
AUTHOR
Patrick De Geest, Aug 15 1998
EXTENSIONS
Simplified definition by Sean A. Irvine, Mar 29 2010
a(5) from Sean A. Irvine, Mar 29 2010
STATUS
approved