A217062 Primes that remain prime when a single "9" digit is inserted between any two adjacent digits.

11, 13, 17, 19, 23, 37, 41, 53, 59, 61, 97, 101, 107, 113, 149, 193, 197, 199, 227, 239, 263, 269, 271, 311, 331, 367, 409, 431, 443, 457, 499, 587, 617, 659, 661, 691, 727, 733, 751, 823, 863, 941, 967, 1009, 1423, 1571, 1709, 1759, 1973, 1993, 1997, 2063, 2137

Offset: 1

Author

Paolo P. Lava, Sep 26 2012

Keywords

• nonn
• base

Examples

			214883 is prime and also 2148893, 2148983, 2149883, 2194883 and 2914883.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..236

Crossrefs

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217047, A217063-A217065

Programs

Maple

with(numtheory);
A217062:=proc(q,x)
local a,b,c,i,n,ok;
for n from 5 to q do
  a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=ithprime(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(ithprime(n)); fi; od; end:
A217062(1000000,9);

PARI

is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=9; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012