A095056 Number of primes with three 1-bits (A081091) in range [2^n,2^(n+1)].
0, 1, 2, 1, 2, 3, 3, 0, 4, 2, 3, 2, 2, 2, 4, 1, 3, 4, 5, 3, 2, 1, 5, 1, 0, 2, 5, 2, 2, 8, 6, 0, 5, 3, 4, 2, 3, 2, 2, 0, 3, 5, 0, 1, 5, 3, 7, 0, 1, 2, 5, 1, 5, 2, 6, 0, 6, 0, 2, 3, 2, 1, 2, 0, 2, 3, 5, 3, 6, 2, 2, 2, 5, 2, 7, 1, 3, 2, 3, 1, 6, 2, 4, 3, 3, 2, 6, 1, 1, 5, 7, 2, 4, 2, 5, 0, 3, 4, 3, 1, 2, 1, 3, 0, 5
Offset: 1
Keywords
Examples
From _Michael De Vlieger_, Feb 27 2017: (Start) a(1) = 0 because there are no primes with three 1s in binary expansion between 2^1 and 2^2. a(2) = 1 since the only prime between 2^2 and 2^3 with three 1s in binary expansion is 7 = binary 111. a(3) = 2 since between 2^3 and 2^4 we have 11 and 13 (binary 1011 and 1101, respectively) have three 1s. (End)
Links
- T. D. Noe, Table of n, a(n) for n=1..1000
- A. Karttunen and J. Moyer, C-program for computing the initial terms of this sequence
- Samuel S. Wagstaff, Jr., Prime Numbers with a fixed number of one bits or zero bits in their binary representation, Exp. Math. vol. 10, issue 2 (2001) 267, Table 2. - From _N. J. A. Sloane_, Jun 19 2011.
- Index entries for sequences related to occurrences of various subsets of primes in range ]2^n,2^(n+1)]
Programs
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Mathematica
Table[m = Count[Prime@ Range[PrimePi[2^n] + 1, PrimePi[2^(n + 1) - 1]], k_ /; DigitCount[k, 2, 1] == 3]; Print@ m; m, {n, 24}] (* Michael De Vlieger, Feb 27 2017 *)
Extensions
More terms from T. D. Noe, Oct 17 2007