A053795 -id:A053795 - cp's OEIS frontend

A158725 Non-repdigit composite numbers not divisible by 2, 3, 5 or 11.

49, 91, 119, 133, 161, 169, 203, 217, 221, 247, 259, 287, 289, 299, 301, 323, 329, 343, 361, 371, 377, 391, 403, 413, 427, 437, 469, 481, 493, 497, 511, 527, 529, 533, 551, 553, 559, 581, 589, 611, 623, 629, 637, 667, 679, 689, 697, 703, 707, 713, 721, 731

Offset: 1

Lekraj Beedassy, Mar 24 2009

nonn

Non-repdigit composite numbers ending in 1, 3, 7 or 9, with digital root not a multiple of 3 and whose alternate digit sums do not differ by a multiple of 11.
The "compositeness" of larger entries of the sequence is not obvious right away or deducible by mere inspection, and hence these terms readily lend themselves to be (erroneously) suspected as primes to the casual glance.
This differs from the corresponding sequence without the repunit condition starting at a(1351) = 11123 rather than 11111. - Charles R Greathouse IV, Sep 08 2012

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A007775, A053795, A008364.

is(n)=gcd(n,330)==1&&!isprime(n)&&n%(10^#Str(n)\9) \\ Charles R Greathouse IV, Sep 08 2012

a(n) ~ kn with k = 33/8. - Charles R Greathouse IV, Sep 08 2012

Corrected and extended by Ray Chandler, Mar 27 2009

A216167 Composite numbers which yield a prime whenever a 5 is inserted anywhere in them, excluding at the end.

Original entry on oeis.org

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

Offset: 1

Paolo P. Lava, Sep 03 2012

			4083 is not prime but 40853, 40583, 45083 and 54083 are all primes.

Michael S. Branicky, Table of n, a(n) for n = 1..1923 (terms 1..300 from Paolo P. Lava)

Cf. A068673, A068674, A068677, A068679, A069246, A215417, A215419-A215421, A216165, A216166, A216168, A216169.

Subsequence of A053795.

[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

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);

Select[Range[6000],CompositeQ[#]&&AllTrue[FromDigits/@Table[Insert[IntegerDigits[#],5,p],{p,IntegerLength[#]}],PrimeQ]&] (* Harvey P. Dale, Oct 02 2022 *)

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

A100490 Odd numbers ending in {1,3,7,9} that are not primes.

Original entry on oeis.org

1, 9, 21, 27, 33, 39, 49, 51, 57, 63, 69, 77, 81, 87, 91, 93, 99, 111, 117, 119, 121, 123, 129, 133, 141, 143, 147, 153, 159, 161, 169, 171, 177, 183, 187, 189, 201, 203, 207, 209, 213, 217, 219, 221, 231, 237, 243, 247, 249, 253, 259, 261, 267, 273, 279, 287

Offset: 0

Roger L. Bagula, Nov 22 2004

nonn

Essentially the same as A053795. [From R. J. Mathar, Sep 02 2008]

Select[Range[1,311,2],MemberQ[{1,3,7,9},Mod[#,10]]&&!PrimeQ[#]&] (* Harvey P. Dale, Sep 01 2024 *)

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A158725 Non-repdigit composite numbers not divisible by 2, 3, 5 or 11.

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A216167 Composite numbers which yield a prime whenever a 5 is inserted anywhere in them, excluding at the end.

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A100490 Odd numbers ending in {1,3,7,9} that are not primes.

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