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%I #17 Dec 01 2014 21:34:56
%S 26,34,38,39,46,51,52,57,58,62,65,68,69,74,76,78,82,85,86,87,91,92,93,
%T 94,95,102,104,106,114,115,116,117,118,119,122,123,124,129,130,133,
%U 134,136,138,142,143,145,146,148,152,153,155,156,158,159,164
%N Natural numbers that are not (primes, 11-smooth, perfect powers or base-10 palindromes).
%C The intention was to generate a sequence of uninteresting numbers. - _John R Phelan_, Dec 01 2014
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Complement_(set_theory)">Complement (set theory)</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Interesting number paradox">Interesting number paradox</a>
%F A000027 \ A000040 \ A051038 \ A002113 \ A001597.
%F A \ B represents set "subtraction", all the elements in A that are not in B.
%F In other words, start with the Natural numbers (A000027).
%F Remove the prime numbers (A000040).
%F Remove the 11-smooth numbers, numbers whose prime divisors are all <= 11 (A051038).
%F Remove the base-10 palindromes (A002113).
%F Remove the perfect powers, m^k where m > 0 and k >= 2 (A001597).
%F And what's left is this sequence.
%F a(n) ~ n; in particular, a(n) = n + n/log n + o(n/log n). - _Charles R Greathouse IV_, Nov 27 2013
%e 16 is not in the sequence since it's a perfect power, 2^4.
%e 19 is not in the sequence since it's prime.
%e 18 is not in the sequence since it's 2*3*3, so it's 11-smooth.
%e 22 is not in the sequence since it's a base 10 palindrome.
%e 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.
%o (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;}}
%Y This sequence is A000027 \ A000040 \ A051038 \ A002113 \ A001597.
%K base,easy,nonn
%O 1,1
%A _John R Phelan_, Nov 27 2013
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