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A229826 Evil (A001969) numbers divisible by 7 but not divisible by 3. 1
77, 119, 154, 175, 238, 245, 287, 308, 329, 343, 350, 371, 413, 427, 455, 469, 476, 490, 497, 553, 574, 581, 616, 658, 679, 686, 700, 742, 763, 791, 826, 833, 854, 910, 917, 931, 938, 952, 980, 994, 1043, 1085, 1106, 1127, 1141, 1148, 1162, 1169, 1232, 1253 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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.

REFERENCES

J. Coquet, A summation formula related to the binary digits, Invent. Math. 73, no.1 (1983), 107-115.

D. J. Newman, On the number of binary digits in a multiple of three, Proc. of American Mat. Soc. 21, no.3 (1969), 719-721.

LINKS

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

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

MATHEMATICA

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

PROG

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

CROSSREFS

Cf. A001969, A000069, A224072.

Sequence in context: A154534 A235867 A274967 * A330103 A176278 A105998

Adjacent sequences:  A229823 A229824 A229825 * A229827 A229828 A229829

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Sep 30 2013

STATUS

approved

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Last modified February 21 02:02 EST 2020. Contains 332086 sequences. (Running on oeis4.)