A217046 Primes that remain prime when a single "6" digit is inserted between any two adjacent decimal digits.

13, 17, 23, 29, 37, 41, 43, 47, 53, 59, 61, 71, 79, 83, 97, 101, 109, 113, 137, 157, 163, 167, 263, 277, 293, 307, 313, 317, 331, 397, 421, 443, 457, 463, 569, 607, 653, 659, 661, 673, 691, 739, 769, 787, 809, 823, 829, 863, 881, 977, 997, 1063, 1087, 1453

Offset

1,1

Links

Harvey P. Dale, Table of n, a(n) for n = 1..500 (First 262 terms from Paolo P. Lava)

Example

185917 is prime and also 1859167, 1859617, 1856917, 1865917 and 1685917.

Maple

with(numtheory);
A217044:=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:
A217044(100000, 6)

Mathematica

Select[Prime[Range[5, 1200]], And@@PrimeQ[FromDigits/@Table[ Insert[ IntegerDigits[ #], 6, i], {i, 2, IntegerLength[#]}]]&] (* Harvey P. Dale, Oct 09 2012 *)

Prog

(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=6; 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, A217045, A217047, A217062-A217065

Sequence in context: A316603 A235914 A050716 * A141076 A092146 A207991

Adjacent sequences: A217043 A217044 A217045 * A217047 A217048 A217049

Keyword

nonn,base

Author

Paolo P. Lava, Sep 25 2012

Status

approved