A069154 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.

250, 256, 2048, 2176, 2304, 2500, 2560, 2744, 23328, 25000, 25600, 119911, 219488, 236196, 250000, 256000, 262144, 290912, 2097152, 2238728, 2317312, 2359296, 2370816, 2500000, 2560000, 3515625, 3720087, 5117695, 13436683, 21359416, 23592960, 23887872

Offset

1,1

Comments

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?

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..106 (terms < 10^12)

Joseph L. Pe, The Enlightened Numbers

Example

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.

Mathematica

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 *)

Crossrefs

Sequence in context: A371491 A225209 A197363 * A045169 A267856 A268269

Adjacent sequences: A069151 A069152 A069153 * A069155 A069156 A069157

Keyword

base,nonn

Author

Joseph L. Pe, Apr 08 2002

Extensions

Corrected and extended by Giovanni Resta, Apr 01 2013

Status

approved