A046461 Numbers k such that concatenation of numbers from 1 to k is a semiprime.

3, 4, 7, 34, 97

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

Table of n, a(n) for n=1..5.

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

A007908(691)=1304238680165623831238651513722972177904593843651*C1916, so A007908(691) is not a semiprime and 691 is not a term of this sequence.

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

Cf. A007908, A046460.

Sequence in context: A042773 A042173 A317811 * A084590 A279920 A041135

Adjacent sequences: A046458 A046459 A046460 * A046462 A046463 A046464

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