|
%I #6 Feb 11 2014 19:05:27
%S 250,256,2048,2176,2304,2500,2560,2744,23328,25000,25600,119911,
%T 219488,236196,250000,256000,262144,290912,2097152,2238728,2317312,
%U 2359296,2370816,2500000,2560000,3515625,3720087,5117695,13436683,21359416,23592960,23887872
%N Treated as strings, the concatenation c of the prime factors of n, in increasing order, is an initial segment of n. Equivalently, n begins with c.
%C All terms listed above have at most three prime factors. Is there an upper bound to the number of prime factors of terms of this sequence?
%C Called "enlightened numbers" by J. Pe. Note that the Mathematica program he provides in his web page erroneously recognizes some numbers as members of the sequence, for example 2239488. The smallest member with 4 prime factors is 2377970784 = 2^5*3^5*7^2*79^2. - _Giovanni Resta_, Apr 01 2013
%H Giovanni Resta, <a href="/A069154/b069154.txt">Table of n, a(n) for n = 1..106</a> (terms < 10^12)
%H Joseph L. Pe, <a href="http://www.numeratus.net/enlightened/enlightened.html">The Enlightened Numbers</a>
%e The prime factors of 119911 are 11 and 991, which when concatenated yield 11991, an initial segment of 119911. Therefore 119911 is a term of the sequence.
%t seq = {}; Do[If[PrimeQ[n] || EvenQ[n] && IntegerDigits[n][[1]] != 2, Continue[]]; p = StringPosition[ToString@n, StringJoin[ToString /@ First /@ FactorInteger@n]]; If[p != {} && p[[1, 1]] == 1, Print[n]; AppendTo[seq, n]], {n, 2, 10^6}]; seq (* _Giovanni Resta_, Apr 01 2013 *)
%K base,nonn
%O 1,1
%A _Joseph L. Pe_, Apr 08 2002
%E Corrected and extended by _Giovanni Resta_, Apr 01 2013
|
