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A326669 Numbers n such that the average position of a 1 in the binary expansion of n is an integer. 16
1, 2, 4, 5, 7, 8, 10, 14, 16, 17, 20, 21, 27, 28, 31, 32, 34, 35, 39, 40, 42, 49, 54, 56, 57, 62, 64, 65, 68, 70, 73, 78, 80, 84, 85, 93, 98, 99, 107, 108, 112, 114, 119, 124, 127, 128, 130, 133, 136, 140, 141, 146, 147, 155, 156, 160, 161, 167, 168, 170, 175 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

These are numbers whose exponents in their representation as a sum of distinct powers of 2 have integer average.

LINKS

Table of n, a(n) for n=1..61.

EXAMPLE

42 is in the sequence because 42 = 2^1 + 2^3 + 2^5 and the average of {1,3,5} is 3, an integer.

MATHEMATICA

Select[Range[100], IntegerQ[Mean[Join@@Position[IntegerDigits[#, 2], 1]]]&]

CROSSREFS

Cf. A000120, A051293, A070939, A102627, A291165, A291166, A316413, A326622, A326668, A326672, A326673.

Sequence in context: A258376 A231979 A072013 * A123064 A108513 A029749

Adjacent sequences:  A326666 A326667 A326668 * A326670 A326671 A326672

KEYWORD

nonn,base

AUTHOR

Gus Wiseman, Jul 17 2019

STATUS

approved

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Last modified June 23 13:59 EDT 2021. Contains 345402 sequences. (Running on oeis4.)