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, 993, 21161, 588821, 26600591

Offset

1,1

Comments

a(8) > 10^7. - Tyler Busby, Feb 07 2023

a(9) > 10^8. - Daniel Suteu, Feb 08 2023

Links

Table of n, a(n) for n=1..8.

Example

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.

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]

Prog

(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

Crossrefs

Cf. A001358, A056815, A204541.

Sequence in context: A041070 A248263 A201449 * A065938 A131902 A265029

Adjacent sequences: A205297 A205298 A205299 * A205301 A205302 A205303

Keyword

nonn,base,hard,more

Author

Robert G. Wilson v, Jan 27 2012

Extensions

a(7) from Tyler Busby, Feb 07 2023

a(8) from Daniel Suteu, Feb 08 2023

Status

approved