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

1,1

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

Formula

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

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 *)

Prog

(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

Crossrefs

Subsequence of A045572.

Sequence in context: A338909 A173456 A192192 * A100490 A173250 A128462

Adjacent sequences: A053792 A053793 A053794 * A053796 A053797 A053798

Keyword

nonn,base,easy

Author

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

Extensions

More terms from James A. Sellers, Apr 08 2000

Offset corrected by Arkadiusz Wesolowski, Dec 18 2011

Status

approved