A216169 Composite numbers > 9 which yield a prime whenever a 0 is inserted between any two digits.

49, 119, 121, 133, 161, 169, 203, 253, 299, 301, 319, 323, 403, 407, 473, 493, 511, 539, 551, 581, 611, 667, 679, 713, 869, 901, 913, 943, 1007, 1067, 1079, 1099, 1211, 1273, 1691, 1729, 1799, 1909, 2021, 2047, 2101, 2117, 2359, 2407, 2533, 2717, 2759, 2899

Offset: 1

Author

Paolo P. Lava, Sep 03 2012

Keywords

• nonn
• base

Examples

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

Links

• Paolo P. Lava and Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 1500 terms from Paolo P. Lava)

Crossrefs

Subset of composite numbers in A164329. - M. F. Hasler, May 10 2018

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

Programs

Maple

A216169:=proc(q,x)
local a,b,c,i,n,ok;
for n from 10 to q do
if not isprime(n) then
  a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1;
  for i from 1 to b-1 do c:=a+9*10^i*trunc(a/10^i)+10^i*x;
    if not isprime(c) then ok:=0; break; fi; od;
  if ok=1 then print(n); fi;
fi; od; end: A216169(1000,0);

Mathematica

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 *)

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

Extensions

Name edited by M. F. Hasler, May 10 2018