A179996 - OEIS

A179996

Composite numbers n such that Sum_{k=0..q} d(k)*10^k is prime where d(k) are the q+1 distinct prime factors of n, d(0)< d(1) < ... < d(q).

%I #10 Sep 02 2022 18:29:29

%S 15,21,33,45,51,57,63,69,75,87,91,93,99,111,129,133,135,147,153,165,

%T 171,177,183,187,189,201,207,217,219,225,253,255,261,273,279,297,303,

%U 309,327,333,363,375,387,399,405,411,427

%N Composite numbers n such that Sum_{k=0..q} d(k)*10^k is prime where d(k) are the q+1 distinct prime factors of n, d(0)< d(1) < ... < d(q).

%e 435 is in the sequence because the prime divisors of 435 are {3, 5, 29} and

%e 3 + 5*10 + 29*100 = 2953 is prime.

%p with(numtheory):T:=array(1..10) : for n from 1 to 1000 do:x:=factorset(n):

%p k:=nops(x):s:=0:for i from 1 to k do:s:=s+x[i]*10^(i-1) :od:if type(s,prime)=true

%p and k > 1 then printf(`%d, `, n):else fi:od:

%t cnpQ[n_]:=Module[{pd=FactorInteger[n][[All,1]]},Length[pd]>1&&PrimeQ[ Total[ pd*10^Range[0,Length[pd]-1]]]]; Select[Range[500],cnpQ] (* _Harvey P. Dale_, Sep 02 2022 *)

%K nonn,base

%O 1,1

%A _Michel Lagneau_, Jan 13 2011