1,1

By the Moser-Newman phenomenon, among the first N positive integers divisible by 3, the evil numbers are always in the majority. But what happens if we remove from the positive numbers the multiples of 3? We conjecture that in this case we obtain another phenomenon: among the first N such positive integers divisible by 7, the odious numbers (A000069) are always in the majority.

Harvey P. Dale, Table of n, a(n) for n = 1..1000

J. Coquet, A summation formula related to the binary digits, Inventiones Mathematicae 73 (1983), pp. 107-115.

D. J. Newman, On the number of binary digits in a multiple of three, Proc. Amer. Math. Soc. 21 (1969) 719-721.

Vladimir Shevelev, Generalized Newman phenomena and digit conjectures on primes, Internat. J. of Mathematics and Math. Sciences, 2008 (2008), Article ID 908045, 1-12.

With[{evil=Select[Range[0, 1500], EvenQ[DigitCount[#, 2, 1]]&]}, Select[evil, Divisible[#, 7]&&!Divisible[#, 3]&]] (* Harvey P. Dale, Dec 04 2014 *)

(PARI) is(n)=hammingweight(n)%2==0 && gcd(n, 21)==7 \\ Charles R Greathouse IV, Sep 30 2013

Cf. A001969, A000069, A224072.

Sequence in context: A154534 A235867 A274967 * A330103 A176278 A105998

Adjacent sequences: A229823 A229824 A229825 * A229827 A229828 A229829

nonn,base

Vladimir Shevelev, Sep 30 2013

approved