A225136 - OEIS

%I #13 May 06 2013 11:28:01

%S 88,128,188,208,278,288,308,428,448,458,508,528,638,668,688,708,758,

%T 768,788,808,812,818,820,827,828,830,842,844,845,850,852,863,866,868,

%U 870,875,876,878,888,892,898,899,928,988,998,1028,1058,1108,1148,1168,1178

%N Numbers that are concatenations of triprimes.

%H Christian N. K. Anderson, <a href="/A225136/b225136.txt">Table of n, a(n) for n = 1..10000</a>

%H Christian N. K. Anderson, <a href="/A225136/a225136.txt">Table of n, a(n), all possible separations of a(n) into triprimes</a> for n=1..10000.

%e 88 = 8|8, both of which are triprime because 8=2*2*2.

%e 458 = 45 | 8 = 3*3*5 | 2*2*2.

%e 12428 can be split into triprimes in three ways: 12|428, 12|42|8, and 124|28.

%o (R) library(gmp); istriprime=function(x) ifelse(x<8,F,length(factorize(x))==3)

%o splithasproperty<-function(n,FUN,curdig=1,res=list(),curspl=c()) {

%o no0<-function(s){ while(substr(s,1,1)=="0" & nchar(s)>1) s=substr(s,2,nchar(s)); s}

%o     s=as.character(n)

%o     if(curdig>nchar(s)) return(res)

%o     if(length(curspl)>0) if(FUN(as.bigz(no0(substr(s,curdig,nchar(s)))))) res[[length(res)+1]]=curspl

%o     for(i in curdig:nchar(s))

%o         if(FUN(as.bigz(no0(substr(s,curdig,i)))))

%o             res=splithasproperty(n,FUN,i+1,res,c(curspl,i))

%o     res

%o }

%o which(sapply(1:500,function(x) length(splithasproperty(x,istriprime)))>0)

%Y Cf. A106582, A019549, A030459.

%K nonn,base,less

%O 1,1

%A _Kevin L. Schwartz_ and _Christian N. K. Anderson_, Apr 29 2013