A232668 Natural numbers that are not (primes, 11-smooth, perfect powers or base-10 palindromes).

26, 34, 38, 39, 46, 51, 52, 57, 58, 62, 65, 68, 69, 74, 76, 78, 82, 85, 86, 87, 91, 92, 93, 94, 95, 102, 104, 106, 114, 115, 116, 117, 118, 119, 122, 123, 124, 129, 130, 133, 134, 136, 138, 142, 143, 145, 146, 148, 152, 153, 155, 156, 158, 159, 164

Offset

1,1

Comments

The intention was to generate a sequence of uninteresting numbers. - John R Phelan, Dec 01 2014

Links

Table of n, a(n) for n=1..55.

Wikipedia, Complement (set theory)

Wikipedia, Interesting number paradox

Formula

A000027 \ A000040 \ A051038 \ A002113 \ A001597.

A \ B represents set "subtraction", all the elements in A that are not in B.

In other words, start with the Natural numbers (A000027).

Remove the prime numbers (A000040).

Remove the 11-smooth numbers, numbers whose prime divisors are all <= 11 (A051038).

Remove the base-10 palindromes (A002113).

Remove the perfect powers, m^k where m > 0 and k >= 2 (A001597).

And what's left is this sequence.

a(n) ~ n; in particular, a(n) = n + n/log n + o(n/log n). - Charles R Greathouse IV, Nov 27 2013

Example

16 is not in the sequence since it's a perfect power, 2^4.
19 is not in the sequence since it's prime.
18 is not in the sequence since it's 2*3*3, so it's 11-smooth.
22 is not in the sequence since it's a base 10 palindrome.
26 is in the sequence since it's 2*13, so it's not prime, not 11-smooth, not a base-10 palindrome, and not a perfect power.

Prog

(Java) public class Nnn {public static void main(String[] args) {String str = ""; for (int i = 0; i < 1000000 && str.length() < 250; i++) {if (isPrime(i) || isSmooth(11, i) || isPerfectPower(i) || isPalindrome(i)) {} else {str += i + ", "; }} System.out.println(str); } static boolean isPalindrome(int i) {return ((i+"").equals(new StringBuilder(i+"").reverse().toString())); } static boolean isSmooth(int s, int n) {if (n<2) return true; for (int i=2; i<=s; i++) {while (n%i==0) n=n/i; } return n==1; } static boolean isPerfectPower(int n) {for (int i=2; i<=Math.sqrt(n); i++) {int j=i*i; while (j<n) j*=i; if (j==n) return true; } return false; } static boolean isPrime(int n) {if (n<2) return false; for (int i=2; i<=Math.sqrt(n); i++) {if (n%i==0) return false; } return true; }}

Crossrefs

This sequence is A000027 \ A000040 \ A051038 \ A002113 \ A001597.

Sequence in context: A129914 A106794 A119481 * A349733 A100393 A133635

Adjacent sequences: A232665 A232666 A232667 * A232669 A232670 A232671

Keyword

base,easy,nonn

Author

John R Phelan, Nov 27 2013

Status

approved