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A217063 Primes that remain prime when a single "3" digit is inserted between any two adjacent decimal digits. 4
11, 17, 19, 23, 29, 31, 37, 41, 43, 61, 73, 79, 89, 97, 101, 103, 127, 167, 173, 181, 211, 233, 239, 251, 271, 283, 307, 331, 359, 373, 439, 491, 509, 523, 547, 599, 673, 709, 733, 769, 877, 887, 937, 941, 991, 1033, 1229, 1381, 1619, 1721, 1759, 1789, 1901 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Bruno Berselli, Table of n, a(n) for n = 1..1000 (first 275 terms from Paolo Lava)
EXAMPLE
212881 is prime and also 2128831, 2128381, 2123881, 213288 and 2312881.
MAPLE
with(numtheory);
A217063:=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:
A217063(1000000, 3);
PROG
(Magma) [p: p in PrimesInInterval(11, 2000) | forall{m: t in [1..#Intseq(p)-1] | IsPrime(m) where m is (Floor(p/10^t)*10+3)*10^t+p mod 10^t}]; // Bruno Berselli, Sep 26 2012
(PARI) is(n)=my(v=concat([""], digits(n))); for(i=2, #v-1, v[1]=Str(v[1], v[i]); v[i]=3; if(i>2, v[i-1]=""); if(!isprime(eval(concat(v))), return(0))); isprime(n) \\ Charles R Greathouse IV, Sep 26 2012
(Python)
from sympy import isprime, primerange
def ok(p):
if p < 10: return False
s = str(p)
return all(isprime(int(s[:i] + "3" + s[i:])) for i in range(1, len(s)))
def aupto(limit): return [p for p in primerange(1, limit+1) if ok(p)]
print(aupto(1901)) # Michael S. Branicky, Nov 17 2021
CROSSREFS
Sequence in context: A063449 A157996 A050713 * A038966 A050778 A316100
KEYWORD
nonn,base
AUTHOR
Paolo P. Lava, Sep 26 2012
STATUS
approved

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Last modified July 23 23:47 EDT 2024. Contains 374575 sequences. (Running on oeis4.)