A168162 Numbers n which do not exceed the sum of the binary digits in all primes <= n.

3, 5, 7, 8, 11, 13, 14, 19, 23, 31, 32, 47, 61

Offset: 1

Author

M. F. Hasler, Nov 22 2009

Keywords

• fini
• full
• nonn
• base

Comments

The sequence A168161 is a subsequence of the primes in this sequence.

Examples

			There is no prime <= 1 and 2 has only nonzero binary digit, therefore these numbers are not in the sequence.
However, a(1)=3 has two binary digits, so the total number of these equal 3.
Then, 4 is larger than this, but the prime p=5 again adds 2 nonzero binary digits adding to a total of 5=a(2).
Then 6 is larger than this, but the prime p=7 adds 3 more nonzero bits for a total of 8, such that a(3)=7 and a(4)=8 don't exceed this.
		

Programs

PARI

s=0; for(n=1,9999, isprime(n) && s+=norml2(binary(n)); n<=s & print1(n", "))

Formula

A168162 = { n | n <= A095375(pi(n)) }, where pi(n) = A000720(n).