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A216167 Composite numbers which yield a prime whenever a 5 is inserted anywhere in them, excluding at the end. 3
9, 21, 57, 63, 69, 77, 87, 93, 153, 231, 381, 407, 413, 417, 501, 531, 581, 651, 669, 741, 749, 783, 791, 987, 1241, 1551, 1797, 1971, 2189, 2981, 3381, 3419, 3591, 3951, 4083, 4503, 4833, 4949, 4959, 5049, 5117, 5201, 5229, 5243, 5529, 5547, 5603, 5691, 5697 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Michael S. Branicky, Table of n, a(n) for n = 1..1923 (terms 1..300 from Paolo P. Lava)
EXAMPLE
4083 is not prime but 40853, 40583, 45083 and 54083 are all primes.
MAPLE
with(numtheory);
A216167:=proc(q, x)
local a, b, c, i, n, ok;
for n from 1 to q do
if not isprime(n) then
a:=n; b:=0; while a>0 do b:=b+1; a:=trunc(a/10); od; a:=n; ok:=1;
for i from 1 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(n); fi;
fi;
od; end:
A216167(1000, 5);
MATHEMATICA
Select[Range[6000], CompositeQ[#]&&AllTrue[FromDigits/@Table[Insert[IntegerDigits[#], 5, p], {p, IntegerLength[#]}], PrimeQ]&] (* Harvey P. Dale, Oct 02 2022 *)
PROG
(Magma) [n: n in [1..6000] | not IsPrime(n) and forall{m: t in [1..#Intseq(n)] | IsPrime(m) where m is (Floor(n/10^t)*10+5)*10^t+n mod 10^t}]; // Bruno Berselli, Sep 03 2012
(Python)
from sympy import isprime
def ok(n):
if n < 2 or n%10 not in {1, 3, 7, 9} or isprime(n): return False
s = str(n)
return all(isprime(int(s[:i] + '5' + s[i:])) for i in range(len(s)))
print(list(filter(ok, range(5698)))) # Michael S. Branicky, Sep 21 2021
CROSSREFS
Subsequence of A053795.
Sequence in context: A134717 A216980 A147169 * A246327 A320896 A127989
KEYWORD
nonn,look,base
AUTHOR
Paolo P. Lava, Sep 03 2012
STATUS
approved

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Last modified April 22 18:11 EDT 2024. Contains 371906 sequences. (Running on oeis4.)