A216169 - OEIS

%I #24 May 17 2018 05:33:58

%S 49,119,121,133,161,169,203,253,299,301,319,323,403,407,473,493,511,

%T 539,551,581,611,667,679,713,869,901,913,943,1007,1067,1079,1099,1211,

%U 1273,1691,1729,1799,1909,2021,2047,2101,2117,2359,2407,2533,2717,2759,2899

%N Composite numbers > 9 which yield a prime whenever a 0 is inserted between any two digits.

%H Paolo P. Lava and Giovanni Resta, <a href="/A216169/b216169.txt">Table of n, a(n) for n = 1..10000</a> (first 1500 terms from Paolo P. Lava)

%e 2359 is not prime but 23509, 23059 and 20359 are all primes.

%p A216169:=proc(q,x)

%p local a,b,c,i,n,ok;

%p for n from 10 to q do

%p if not isprime(n) then

%p   a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1;

%p   for i from 1 to b-1 do c:=a+9*10^i*trunc(a/10^i)+10^i*x;

%p     if not isprime(c) then ok:=0; break; fi; od;

%p   if ok=1 then print(n); fi;

%p fi; od; end: A216169(1000,0);

%t Select[Range[10,3000],CompositeQ[#]&&AllTrue[Table[FromDigits[ Insert[ IntegerDigits[ #],0,n]],{n,2,IntegerLength[#]}],PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 13 2018 *)

%o (PARI) is(n, L=logint(n+!n, 10)+1, P)={!isprime(n) && !for(k=1, L-1, isprime([10*P=10^(L-k),1]*divrem(n, P))||return) && n>9} \\ _M. F. Hasler_, May 10 2018

%Y Subset of composite numbers in A164329. - _M. F. Hasler_, May 10 2018

%Y Cf. A068673, A068674, A068677, A068679, A069246, A215417, A215419-A215421, A216165-A216168.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Sep 03 2012

%E Name edited by _M. F. Hasler_, May 10 2018