A066349 - OEIS

A066349

A self-generating sequence: let S = {}, a(0) = 333; for n >= 1, factorize a(n-1), arrange prime factors in increasing order and append their digits to S; then a(n) is the 3-digit number formed from terms 3n, 3n+1, 3n+2 of S. Leading zeros are omitted from a(n).

%I #1 May 16 2003 03:00:00

%S 333,735,775,531,335,956,722,239,219,192,393,732,222,223,313,122,361,

%T 233,722,331,326,119,192,332,191,933,121,637,172,222,223,228,319,133,

%U 111,111,771,322,432,337,223,223,191,129,719,337,337,325

%N A self-generating sequence: let S = {}, a(0) = 333; for n >= 1, factorize a(n-1), arrange prime factors in increasing order and append their digits to S; then a(n) is the 3-digit number formed from terms 3n, 3n+1, 3n+2 of S. Leading zeros are omitted from a(n).

%C 333 is the unique 3-digit starting value that produces nontrivial sequences. This is one of the two possible continuations if one starts with 333. For the other see A066801.

%e The factorizations of the first few terms are 3*3*37, 3*5*7*7, 5*5*31, 3*3*59, 5*67, 2*2*239, ... Thus S = [3,3,3,7,3,5,7,7,5,...] and grouping these in sets of three we recover the sequence.

%K base,easy,nonn,nice

%O 0,1

%A Evans A Criswell (criswell(AT)itsc.uah.edu), Dec 19 2001