VOOZH about

URL: https://oeis.org/A217064

⇱ A217064 - OEIS

login
A217064
Primes that remain prime when a single "5" digit is inserted between any two adjacent decimal digits.
3
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
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Sep 26 2012
STATUS
approved