A215419 - OEIS

%I #24 Dec 21 2023 10:23:35

%S 7,11,17,31,37,73,271,331,359,373,673,733,1033,2297,3119,3461,3923,

%T 5323,5381,5419,6073,6353,9103,9887,18289,23549,25349,31333,32933,

%U 33349,35747,37339,37361,37489,47533,84299,92333,93241,95093,98491,133733,136333,139333

%N Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit.

%H Robert Israel, <a href="/A215419/b215419.txt">Table of n, a(n) for n = 1..150</a>

%e 18289 is prime and also 182893, 182839, 182389, 183289, 138289, 318289.

%p A215419:=proc(q,x)

%p local a,b,c,d,i,n,ok;

%p for n from 1 to q do

%p   a:=ithprime(n); b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od;

%p   a:=ithprime(n); ok:=1;

%p   for i from 0 to b do

%p     c:=a+9*10^i*trunc(a/10^i)+10^i*x; if not isprime(c) then ok:=0; break; fi;

%p   od;

%p   if ok=1 then print(ithprime(n)); fi;

%p od; end:

%p A215419(1000,3);

%p # Alternative:

%p filter:= proc(n) local L,d,k,M;

%p if not isprime(n) then return false fi;

%p L:= convert(n,base,10);

%p d:= nops(L);

%p for k from 0 to d do

%p    M:= [seq(L[i],i=1..k),3,seq(L[i],i=k+1..d)];

%p    if not isprime(add(M[i]*10^(i-1),i=1..d+1)) then return false fi;

%p od;

%p true

%p end proc;

%p select(filter, [seq(i,i=3..2*10^5,2)]); # _Robert Israel_, Oct 09 2017

%t ins@n_:=Insert[IntegerDigits@n,3,#]&/@Range@(IntegerLength@n+1);

%t Cases[{#,FromDigits@#&/@ins@#}&/@ Cases[Range[11,70000],_?PrimeQ], {_,{_?PrimeQ..}}][[All,1]] (* _Hans Rudolf Widmer_, Dec 21 2023 *)

%Y Cf. A215417, A069246, A215420, A215421

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Aug 10 2012