A205300 Least semiprime for which n-1 iterations of "Look & Say" (A045918) all yield semiprimes, but not the n-th iteration.
6, 14, 4, 119, 933, 21161, 588821, 26600591
Offset: 1
Examples
All of the following are the least semiprime with the required characteristics. a(1) = 6 because 6 is a semiprime and its 'Look & Say' transformation A045918(6) = 16 is not a semiprime. (The smaller semiprime 4 yields LS(4)=14 which is again a semiprime.) a(2) = 14 because both 14 and A045918(14)=1114 are semiprimes but LS(1114)=3114 is not. a(3) = 4 because 4 (2*2), 14 (2*7) and 1114 (2*557) are all semiprimes but 3114 (2*3*3*173) is not.
Programs
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Mathematica
LookAndSayA[n_] := FromDigits@ Flatten@ IntegerDigits@ Flatten[ Through[ {Length, First}[#]] & /@ Split@ IntegerDigits@ n]; semiPrimeQ[n_] := Plus @@ Last /@ FactorInteger@ n == 2; f[n_] := Block[{k = 1, truth = Append[Table[True, {n}], False]}, While[ semiPrimeQ@# & /@ NestList[ LookAndSayA, k, n] != truth, k++]; k] -
PARI
A205300(n) = for(a=4,1e9,bigomega(a)==2||next; my(t=a); for(k=2,n, bigomega(t=A045918(t))!=2 && next(2)); bigomega(A045918(t))==2 || return(a)) \\ M. F. Hasler, Jan 30 2012
Extensions
a(7) from Tyler Busby, Feb 07 2023
a(8) from Daniel Suteu, Feb 08 2023
a(5) corrected by Giovanni Resta, May 12 2025
Comments