login
Smallest prime factor of n-th term in Look and Say sequence A005150, with a(1)=1.
4

%I #34 Jan 31 2023 20:46:25

%S 1,11,3,7,11,312211,13112221,11,5581,26966089,7,20328937,29,3,3,3,

%T 1637,103,50593,43,13,19,17,103,31,19,7,3,19,1208033,23,3,3,83,3,233,

%U 3,3

%N Smallest prime factor of n-th term in Look and Say sequence A005150, with a(1)=1.

%C The terms in A005150 that are known to be primes are a(2) = 11, a(6) = 312211 and a(7) = 13112221 (A100108).

%C a(n) = 3 iff A004977(n) is positive and divisible by 3.

%C a(39) > 2*10^9. a(62) > 10^7. - _Tyler Busby_, Jan 25 2023

%H Tyler Busby, <a href="/A334132/a334132.txt">Table of n, a(n) for n = 1..75 with -1 for those entries where a(n) has not yet been found</a>, Jan 25 2023.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Look-and-say_sequence">Look-and-say sequence</a>

%F a(n) = A020639(A005150(n)).

%e A005150(7) = 13112221 is prime and a(7) = 13112221.

%e A005150(9) = 31131211131221 = 5581 * 5578070441, hence a(9) = 5581.

%Y Cf. A004977 (sum of digits of terms of A005150), A005150 (Look and Say sequence), A020639, A079562, A100108 (primes in A005150).

%K nonn,base,more

%O 1,2

%A _Bernard Schott_, Apr 15 2020

%E a(17)-a(38) from _Jinyuan Wang_, Apr 15 2020