login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A215419 Primes that remain prime when a single digit 3 is inserted between any two consecutive digits or as the leading or trailing digit. 25
7, 11, 17, 31, 37, 73, 271, 331, 359, 373, 673, 733, 1033, 2297, 3119, 3461, 3923, 5323, 5381, 5419, 6073, 6353, 9103, 9887, 18289, 23549, 25349, 31333, 32933, 33349, 35747, 37339, 37361, 37489, 47533, 84299, 92333, 93241, 95093, 98491, 133733, 136333, 139333 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
EXAMPLE
18289 is prime and also 182893, 182839, 182389, 183289, 138289, 318289.
MAPLE
A215419:=proc(q, x)
local a, b, c, d, i, n, ok;
for n from 1 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 0 to b 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:
A215419(1000, 3);
# Alternative:
filter:= proc(n) local L, d, k, M;
if not isprime(n) then return false fi;
L:= convert(n, base, 10);
d:= nops(L);
for k from 0 to d do
M:= [seq(L[i], i=1..k), 3, seq(L[i], i=k+1..d)];
if not isprime(add(M[i]*10^(i-1), i=1..d+1)) then return false fi;
od;
true
end proc;
select(filter, [seq(i, i=3..2*10^5, 2)]); # Robert Israel, Oct 09 2017
MATHEMATICA
ins@n_:=Insert[IntegerDigits@n, 3, #]&/@Range@(IntegerLength@n+1);
Cases[{#, FromDigits@#&/@ins@#}&/@ Cases[Range[11, 70000], _?PrimeQ], {_, {_?PrimeQ..}}][[All, 1]] (* Hans Rudolf Widmer, Dec 21 2023 *)
CROSSREFS
Sequence in context: A068674 A156112 A158594 * A107642 A079651 A178386
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Aug 10 2012
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified July 14 05:06 EDT 2024. Contains 374291 sequences. (Running on oeis4.)