A184907 Let S_n be the set of the integers having alternating bit sum equal to n. There are a(n) primes among the smallest 2n+1 numbers of S_n.

0, 1, 4, 0, 4, 7, 0, 4, 5, 0, 1, 6, 0, 9, 3, 0, 6, 5, 0, 8, 5, 0, 3, 2, 0, 6, 3, 0, 3, 9, 0, 5, 5, 0, 3, 6, 0, 5, 2, 0, 8, 6, 0, 8, 6, 0, 2, 12, 0, 8, 1, 0, 2, 7, 0, 2, 1, 0, 4, 5, 0, 7, 5, 0, 8, 6, 0, 7, 6, 0, 3, 9, 0, 4, 11, 0, 4, 5, 0, 5, 2

Offset

0,3

Links

Table of n, a(n) for n=0..80.

W. Bomfim, A method to find the first 2n+1 integers having alternating bit sum equal to n

Example

The smallest 2n+1 = 5 numbers of the set S_2 of the integers having alternating bit sum 2, are 5, 17, 20, 23, and 29, so a(2)=4.

Prog

(PARI)II()={i = (4^n - 1)/3 - 2^(2*n-2) + 2^(2*n); if(isprime(i), an++)};
III()={w = 2^(2*n-2); for(j=1, n-1, i += w; w /= 4; i -= w; if(isprime(i), an++; ))};
IV()={i+=3; if(isprime(i), an++); w=2; for(j=1, n-1, i -= w; w *= 4; i+=w; if(isprime(i), an++))};
print1("0, 1, 4, "); for(n=3, 80, an=0; II(); III(); IV(); print1(an, ", ")) \\ Washington Bomfim, Jan 25 2011

Crossrefs

Cf. A065359, A065084, A002450.

Sequence in context: A303560 A341481 A135011 * A127751 A028602 A111767

Adjacent sequences: A184904 A184905 A184906 * A184908 A184909 A184910

Keyword

nonn

Author

Washington Bomfim, Jan 25 2011

Status

approved