|
%I #22 Mar 03 2023 11:56:14
%S 1,2,40,242,842,1541,75067
%N Integer lengths of log(10)-primes.
%C Next term > 76902. - _Eric W. Weisstein_, Oct 12 2015
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConstantPrimes.html">Constant Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/NaturalLogarithmof10Digits.html">Natural Logarithm of 10 Digits</a>
%F a(n) = IntegerLength(A228241(n)).
%e log(10) = 2.302585093..., so
%e a(1) = 1 (1-digit number 2 is prime),
%e a(2) = 2 (2-digit number 23 is a prime),
%e a(3) = 40 (40-digit number 2302585092994045684017991454684364207601 is prime).
%t Module[{nn=2000,lg10},lg10=RealDigits[Log[10],10,nn][[1]];IntegerLength/@ Select[Table[FromDigits[Take[lg10,n]],{n,nn}],PrimeQ]] (* _Harvey P. Dale_, Jul 16 2015 *)
%Y Cf. A228241 (log(10)-primes).
%Y Cf. A002392 (decimal digits of log(10)).
%K nonn,base,more
%O 1,2
%A _Eric W. Weisstein_, Aug 17 2013
%E a(7) from _Eric W. Weisstein_, Oct 12 2015
| 