A053795 Composite numbers ending in 1, 3, 7 or 9.

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: 1

Author

G. L. Honaker, Jr., Apr 01 2000

Keywords

• nonn
• base
• easy

Comments

Composite numbers not divisible by 2 or 5. - Lekraj Beedassy, Jul 05 2004

Composite numbers ending in 1, 3, 7 or 9 are values (some shared within sets, because some values are numbers with multiple factors) of the following sets of binomial products:

{(10x+3)*(10y+7), (10x+9)*(10y+9), (10x+11)*(10y+11)}, {(10x+3)*(10y+11), (10x+7)*(10y+9)},

{(10x+3)*(10y+9), (10x+7)*(10y+11)}, and

{(10x+3)*(10y+3), (10x+7)*(10y+7), (10x+9)*(10y+11)}, with x, y integers >= 0. - Marvin Y. Hubble, Jul 12 2013 and May 12 2014 and Sep 27 2019

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A045572.

Programs

Maple

remove(isprime, [seq(seq(10*i+j,j=[3,7,9,11]),i=0..100)]); # Robert Israel, Jan 29 2018

Mathematica

Select[Range[300],CompositeQ[#]&&OddQ[#]&&!Divisible[#,5]&] (* Harvey P. Dale, Jul 13 2014 *)

PARI

is(n)=gcd(n,10)==1 && !isprime(n) && n>1 \\ Charles R Greathouse IV, Jan 30 2018

Python

from sympy import isprime
def ok(n): return n > 1 and n%10 in {1, 3, 7, 9} and not isprime(n)
print(list(filter(ok, range(2, 288)))) # Michael S. Branicky, Sep 21 2021

Formula

a(n) = 2.5n + 2.5n/log n + O(n/log^2 n). - Charles R Greathouse IV, Jan 30 2018

Extensions

More terms from James Sellers, Apr 08 2000

Offset corrected by Arkadiusz Wesolowski, Dec 18 2011