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

1,1

Links

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

Example

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

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 *)

Prog

(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

Crossrefs

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

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

Sequence in context: A373734 A044236 A044617 * A348054 A090095 A163245

Adjacent sequences: A216166 A216167 A216168 * A216170 A216171 A216172

Keyword

nonn,base

Author

Paolo P. Lava, Sep 03 2012

Extensions

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

Status

approved