A217064 Primes that remain prime when a single "5" digit is inserted between any two adjacent decimal digits.

11, 17, 47, 71, 83, 89, 149, 167, 179, 251, 257, 293, 347, 359, 383, 419, 461, 467, 491, 557, 563, 569, 653, 773, 911, 1193, 1217, 1277, 1451, 1559, 1667, 1823, 1901, 2243, 2309, 2357, 2579, 2657, 2999, 3527, 3533, 4289, 5051, 5351, 5501, 5843, 6089, 6551, 6581

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500 (* First 140 terms from Paolo P. Lava *)

Example

290183  is prime and also 2901853, 2901583, 2905183, 2950183 and 2590183.

Maple

with(numtheory);
A217064:=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:
A217064(1000000, 5);

Mathematica

Select[Prime[Range[5, 1000]], AllTrue[FromDigits/@Table[ Insert[ IntegerDigits[ #], 5, n], {n, 2, IntegerLength[#]}], PrimeQ]&] (* Harvey P. Dale, Feb 20 2022 *)

Prog

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=5; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Cf. A050674, A050711-A050719, A069246, A159236, A215417, A215419-A215421, A217044-A217047, A217062, A217063, A217065

Sequence in context: A248482 A267772 A046122 * A242244 A228031 A324795

Adjacent sequences: A217061 A217062 A217063 * A217065 A217066 A217067

Keyword

nonn,base

Author

Paolo P. Lava, Sep 26 2012

Status

approved